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Journal articles on the topic 'Infinite groups : Group theory'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Li, Fu-Bin. "RETRACTED: The crystallographic group of infinite Coxeter groups." Journal of Algebra 146, no. 1 (1992): 190–204. http://dx.doi.org/10.1016/0021-8693(92)90062-q.

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2

Jespers, E., and S. O. Juriaans. "Isomorphisms of Integral Group Rings of Infinite Groups." Journal of Algebra 223, no. 1 (2000): 171–89. http://dx.doi.org/10.1006/jabr.1999.7989.

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3

Boyer, Robert. "Character theory of infinite wreath products." International Journal of Mathematics and Mathematical Sciences 2005, no. 9 (2005): 1365–79. http://dx.doi.org/10.1155/ijmms.2005.1365.

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The representation theory of infinite wreath product groups is developed by means of the relationship between their group algebras and conjugacy classes with those of the infinite symmetric group. Further, since these groups are inductive limits of finite groups, their finite characters can be classified as limits of normalized irreducible characters of prelimit finite groups. This identification is called the “asymptotic character formula.” TheK0-invariant of the groupC∗-algebra is also determined.

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4

Dixon, M. R., L. A. Kurdachenko, N. N. Semko, and I. Ya Subbotin. "On some topics in the theory of infinite dimensional linear groups." Algebra and Discrete Mathematics 29, no. 1 (2020): 1–32. http://dx.doi.org/10.12958/adm1516.

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5

Chang, Wonjun, Byung Chun Kim, and Yongjin Song. "An infinite family of braid group representations in automorphism groups of free groups." Journal of Knot Theory and Its Ramifications 29, no. 10 (2020): 2042007. http://dx.doi.org/10.1142/s0218216520420079.

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The [Formula: see text]-fold ([Formula: see text]) branched coverings on a disk give an infinite family of nongeometric embeddings of braid groups into mapping class groups. We, in this paper, give new explicit expressions of these braid group representations into automorphism groups of free groups in terms of the actions on the generators of free groups. We also give a systematic way of constructing and expressing these braid group representations in terms of a new gadget, called covering groupoid. We prove that each generator [Formula: see text] of braid group inside mapping class group indu

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6

Connolly, Francis X., and Stratos Prassidis. "On the Exponent of the NK0-Groups of Virtually Infinite Cyclic Groups." Canadian Mathematical Bulletin 45, no. 2 (2002): 180–95. http://dx.doi.org/10.4153/cmb-2002-021-0.

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AbstractIt is known that the K-theory of a large class of groups can be computed from the K-theory of their virtually infinite cyclic subgroups. On the other hand, Nil-groups appear to be the obstacle in calculations involving the K-theory of the latter. The main difficulty in the calculation of Nil-groups is that they are infinitely generated when they do not vanish. We develop methods for computing the exponent of NK0-groups that appear in the calculation of the K0-groups of virtually infinite cyclic groups.

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7

Kuku, Aderemi O., and Guoping Tang. "Higher K -theory of group-rings of virtually infinite cyclic groups." Mathematische Annalen 325, no. 4 (2003): 711–26. http://dx.doi.org/10.1007/s00208-002-0397-2.

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8

STADLBAUER, MANUEL, and BERND O. STRATMANN. "Infinite ergodic theory for Kleinian groups." Ergodic Theory and Dynamical Systems 25, no. 4 (2005): 1305–23. http://dx.doi.org/10.1017/s014338570400104x.

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9

Haefner, J. "Graded Morita Theory for Infinite Groups." Journal of Algebra 169, no. 2 (1994): 552–86. http://dx.doi.org/10.1006/jabr.1994.1297.

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10

Toledo, Domingo. "Book Review: Geometric group theory, Vol. 2: Asymptotic invariants of infinite groups." Bulletin of the American Mathematical Society 33, no. 03 (1996): 395–99. http://dx.doi.org/10.1090/s0273-0979-96-00669-6.

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11

Palacín, Daniel. "Finite rank and pseudofinite groups." Journal of Group Theory 21, no. 4 (2018): 583–91. http://dx.doi.org/10.1515/jgth-2018-0007.

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AbstractIt is proven that an infinite finitely generated group cannot be elementarily equivalent to an ultraproduct of finite groups of a given Prüfer rank. Furthermore, it is shown that an infinite finitely generated group of finite Prüfer rank is not pseudofinite.

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12

Obraztsov, Viatcheslav N. "On infinite complete groups." Communications in Algebra 22, no. 14 (1994): 5875–87. http://dx.doi.org/10.1080/00927879408825167.

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13

Rhemtulla, Akbar, and Said Sidki. "Factorizable infinite solvable groups." Journal of Algebra 122, no. 2 (1989): 397–409. http://dx.doi.org/10.1016/0021-8693(89)90225-1.

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14

Collins, Michael J. "Some infinite Frobenius groups." Journal of Algebra 131, no. 1 (1990): 161–65. http://dx.doi.org/10.1016/0021-8693(90)90170-s.

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15

Berrick, A. J., and C. F. Miller. "Strongly torsion generated groups." Mathematical Proceedings of the Cambridge Philosophical Society 111, no. 2 (1992): 219–29. http://dx.doi.org/10.1017/s0305004100075319.

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It has long been known that the integral homology of a non-trivial finite group must be non-zero in infinitely many dimensions 17. Recent work on the Sullivan conjecture in homotopy theory has made it possible to extend this result to locally finite groups. For more general groups with torsion it becomes more difficult to make such a strong statement. Nevertheless we prove that when a non-perfect group is generated by torsion elements its integral homology must also be non-zero in infinitely many dimensions. Remarkably, this result is best possible, in that for perfect torsion generated groups

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16

Obata, Nobuaki. "A note on certain permutation groups in the infinite dimensional rotation group." Nagoya Mathematical Journal 109 (March 1988): 91–107. http://dx.doi.org/10.1017/s0027763000002786.

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In his book P. Lévy discussed certain permutation groups of natural numbers in connection with the theory of functional analysis. Among them the group , called the Lévy group after T. Hida, has been studied along with Hida’s theory of white noise analysis and has become very important keeping profound contact with the Lévy Laplacian which is an infinite dimensional analogue of the ordinary Laplacian.

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17

DIEKERT, VOLKER, and ALEXEI MYASNIKOV. "GROUP EXTENSIONS OVER INFINITE WORDS." International Journal of Foundations of Computer Science 23, no. 05 (2012): 1001–19. http://dx.doi.org/10.1142/s0129054112400424.

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Non-Archimedean words have been introduced as a new type of infinite words which can be investigated through classical methods in combinatorics on words due to a length function. The length function, however, takes values in the additive group of polynomials ℤ[t] (and not, as traditionally, in ℕ), which yields various new properties. Non-Archimedean words allow to solve a number of interesting algorithmic problems in geometric and algorithmic group theory. There is also a connection to logic and the first-order theory in free groups (Tarski Problems). In the present paper we provide a general

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18

Milliet, Cédric. "On properties of (weakly) small groups." Journal of Symbolic Logic 77, no. 1 (2012): 94–110. http://dx.doi.org/10.2178/jsl/1327068693.

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AbstractA group is small if it has only countably many complete n-types over the empty set for each natural number n. More generally, a group G is weakly small if it has only countably many complete 1-types over every finite subset of G. We show here that in a weakly small group, subgroups which are definable with parameters lying in a finitely generated algebraic closure satisfy the descending chain conditions for their traces in any finitely generated algebraic closure. An infinite weakly small group has an infinite abelian subgroup, which may not be definable. A small nilpotent group is the

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19

El Badry, Mohammed, Mostafa Alaoui Abdallaoui, and Abdelfattah Haily. "Infinite groups whose group algebras satisfy the converse of Schur’s lemma." Journal of Algebra and Its Applications 18, no. 10 (2019): 1950186. http://dx.doi.org/10.1142/s021949881950186x.

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In this work, we give some necessary and/or sufficient conditions for a group algebra of infinite group to satisfy the converse of Schur’s Lemma. Many classes of groups are investigated such as abelian groups, hypercentral groups, groups having abelian subgroup of finite index and finitely generated soluble groups.

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20

Hall, J. I. "Infinite alternating groups as finitary linear transformation groups." Journal of Algebra 119, no. 2 (1988): 337–59. http://dx.doi.org/10.1016/0021-8693(88)90064-6.

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21

D'Angeli, Daniele, Dominik Francoeur, Emanuele Rodaro, and Jan Philipp Wächter. "Infinite automaton semigroups and groups have infinite orbits." Journal of Algebra 553 (July 2020): 119–37. http://dx.doi.org/10.1016/j.jalgebra.2020.02.014.

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22

Zhang, Xiaohong, and Xiaoying Wu. "Involution Abel–Grassmann’s Groups and Filter Theory of Abel–Grassmann’s Groups." Symmetry 11, no. 4 (2019): 553. http://dx.doi.org/10.3390/sym11040553.

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In this paper, some basic properties and structure characterizations of AG-groups are further studied. First, some examples of infinite AG-groups are given, and weak commutative, alternative and quasi-cancellative AG-groups are discussed. Second, two new concepts of involution AG-group and generalized involution AG-group are proposed, the relationships among (generalized) involution AG-groups, commutative groups and AG-groups are investigated, and the structure theorems of (generalized) involution AG-groups are proved. Third, the notion of filter of an AG-group is introduced, the congruence re

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23

Hubert, Pascal, and Gabriela Schmithüsen. "Infinite translation surfaces with infinitely generated Veech groups." Journal of Modern Dynamics 4, no. 4 (2010): 715–32. http://dx.doi.org/10.3934/jmd.2010.4.715.

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24

Neeb, Karl-Hermann. "A complex semigroup approach to group algebras of infinite dimensional Lie groups." Semigroup Forum 77, no. 1 (2008): 5–35. http://dx.doi.org/10.1007/s00233-008-9073-5.

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25

Adeleke, S. A. "On Irregular Infinite Jordan Groups." Communications in Algebra 41, no. 4 (2013): 1514–46. http://dx.doi.org/10.1080/00927872.2011.643843.

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26

Bux, Kai-Uwe, and Cora Welsch. "Coset posets of infinite groups." Journal of Group Theory 23, no. 4 (2020): 593–605. http://dx.doi.org/10.1515/jgth-2019-0162.

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AbstractWe consider the coset poset associated with the families of proper subgroups, proper subgroups of finite index and proper normal subgroups of finite index. We investigate under which conditions those coset posets have contractible geometric realizations.

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27

Fuchs, L. "Butler groups of infinite rank." Journal of Pure and Applied Algebra 98, no. 1 (1995): 25–44. http://dx.doi.org/10.1016/0022-4049(95)90015-2.

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28

Wilson, John S. "Large hereditarily just infinite groups." Journal of Algebra 324, no. 2 (2010): 248–55. http://dx.doi.org/10.1016/j.jalgebra.2010.03.023.

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29

Le Maître, François, and Phillip Wesolek. "On strongly just infinite profinite branch groups." Journal of Group Theory 20, no. 1 (2017): 1–32. http://dx.doi.org/10.1515/jgth-2016-0022.

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AbstractFor profinite branch groups, we first demonstrate the equivalence of the Bergman property, uncountable cofinality, Cayley boundedness, the countable index property, and the condition that every non-trivial normal subgroup is open; compact groups enjoying the last condition are called strongly just infinite. For strongly just infinite profinite branch groups with mild additional assumptions, we verify the invariant automatic continuity property and the locally compact automatic continuity property. Examples are then presented, including the profinite completion of the first Grigorchuk g

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30

Juhász, Arye. "On a conjecture in Artin groups." International Journal of Algebra and Computation 31, no. 06 (2021): 1217–41. http://dx.doi.org/10.1142/s0218196721400105.

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It is conjectured that an irreducible Artin group which is of infinite type has trivial center. The conjecture is known to be true for two-dimensional Artin groups and for a few other types of Artin groups. In this work, we show that the conjecture holds true for Artin groups which satisfy a condition stronger than being of infinite type. We use small cancellation theory of relative presentations.

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31

MANTUROV, O. V., and V. O. MANTUROV. "FREE KNOTS AND GROUPS." Journal of Knot Theory and Its Ramifications 19, no. 02 (2010): 181–86. http://dx.doi.org/10.1142/s0218216510007826.

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Free knots are a simplification of virtual knots obtained by forgetting arrow/sign information at classical crossings. First non-trivial examples of free knots were constructed recently by the second named author. By using parity considerations, we construct invariants of free knots valued in certain groups. These groups have a simple combinatorial description, the first one being the infinite dihedral group.

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32

Lockett, D. C., and H. D. Macpherson. "Orbit-equivalent infinite permutation groups." Journal of Algebraic Combinatorics 38, no. 4 (2013): 973–88. http://dx.doi.org/10.1007/s10801-013-0434-0.

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33

Cook, James, and Ronald Fulp. "Infinite-dimensional super Lie groups." Differential Geometry and its Applications 26, no. 5 (2008): 463–82. http://dx.doi.org/10.1016/j.difgeo.2008.04.009.

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34

Qi, Dongwen. "On irreducible, infinite, nonaffine Coxeter groups." Fundamenta Mathematicae 193, no. 1 (2007): 79–93. http://dx.doi.org/10.4064/fm193-1-5.

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35

Cutolo, Giovanni. "Quasi-power automorphisms of infinite groups." Communications in Algebra 21, no. 3 (1993): 1009–23. http://dx.doi.org/10.1080/00927879308824604.

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36

Franciosi, Silvana, Francesco De Giovanni, and Martin L. Newell. "On central automorphisms of infinite groups." Communications in Algebra 22, no. 7 (1994): 2559–78. http://dx.doi.org/10.1080/00927879408824977.

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37

Franciosi, Silvana, Francesco De Giovanni, and Yaroslav P. Sysak. "On ascendant subgroups of infinite groups." Communications in Algebra 26, no. 10 (1998): 3313–33. http://dx.doi.org/10.1080/00927879808826344.

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38

Aljadeff, Eli. "On cohomology rings of infinite groups." Journal of Pure and Applied Algebra 208, no. 3 (2007): 1099–102. http://dx.doi.org/10.1016/j.jpaa.2006.05.015.

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39

Celentani, Maria Rosaria, Giovanni Cutolo, and Antonella Leone. "Groups Whose Infinite Subgroups are Centralizers." Communications in Algebra 37, no. 7 (2009): 2419–30. http://dx.doi.org/10.1080/00927870802304697.

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40

Humphries, Stephen P. "Schur rings over infinite groups II." Journal of Algebra 550 (May 2020): 309–32. http://dx.doi.org/10.1016/j.jalgebra.2020.01.011.

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41

Eliahou, Shalom, and Michel Kervaire. "Minimal sumsets in infinite abelian groups." Journal of Algebra 287, no. 2 (2005): 449–57. http://dx.doi.org/10.1016/j.jalgebra.2005.02.014.

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42

Macpherson, D., and C. E. Praeger. "Cycle Types in Infinite Permutation Groups." Journal of Algebra 175, no. 1 (1995): 212–40. http://dx.doi.org/10.1006/jabr.1995.1184.

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43

Marciniak, Zbigniew S., and Sudarshan K. Sehgal. "Zassenhaus Conjecture and Infinite Nilpotent Groups." Journal of Algebra 184, no. 1 (1996): 207–12. http://dx.doi.org/10.1006/jabr.1996.0256.

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44

Evans, David M., and Elisabetta Pastori. "Second cohomology groups and finite covers of infinite symmetric groups." Journal of Algebra 330, no. 1 (2011): 221–33. http://dx.doi.org/10.1016/j.jalgebra.2010.12.004.

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45

Asri, M. S. M., K. B. Wong, and P. C. Wong. "Fundamental Groups of Graphs of Cyclic Subgroup Separable and Weakly Potent Groups." Algebra Colloquium 28, no. 01 (2021): 119–30. http://dx.doi.org/10.1142/s1005386721000110.

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We give a characterization of the cyclic subgroup separability and weak potency of the fundamental group of a graph of polycyclic-by-finite groups and free-by-finite groups amalgamating edge subgroups of the form [Formula: see text], where [Formula: see text] has infinite order and [Formula: see text] is finite.

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46

Dudkin, Fedor A., and Andrey S. Mamontov. "On knot groups acting on trees." Journal of Knot Theory and Its Ramifications 29, no. 09 (2020): 2050062. http://dx.doi.org/10.1142/s0218216520500625.

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A finitely generated group [Formula: see text] acting on a tree with infinite cyclic edge and vertex stabilizers is called a generalized Baumslag–Solitar group (GBS group). We prove that a one-knot group [Formula: see text] is a GBS group if and only if [Formula: see text] is a torus knot group, and describe all n-knot GBS groups for [Formula: see text].

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47

Nishinaka, Tsunekazu. "Group rings of proper ascending HNN extensions of countably infinite free groups are primitive." Journal of Algebra 317, no. 2 (2007): 581–92. http://dx.doi.org/10.1016/j.jalgebra.2007.09.001.

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48

Levitt, Gilbert. "Quotients and subgroups of Baumslag–Solitar groups." Journal of Group Theory 18, no. 1 (2015): 1–43. http://dx.doi.org/10.1515/jgth-2014-0028.

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AbstractWe determine all generalized Baumslag–Solitar groups (finitely generated groups acting on a tree with all stabilizers infinite cyclic) which are quotients of a given Baumslag–Solitar group BS(

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49

Shami, Ziv. "Coordinatisation by binding groups and unidimensionality in simple theories." Journal of Symbolic Logic 69, no. 4 (2004): 1221–42. http://dx.doi.org/10.2178/jsl/1102022220.

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Abstract.In a simple theory with elimination of finitary hyperimaginaries if tp(a) is real and analysable over a definable set Q, then there exists a finite sequence (ai \ i ≤ n*) ⊆ dcleq(a) with an* = a such that for every i ≤ n* if pi = tp(ai/{aj |j < i}) then Aut(pi / Q) is type-definable with its action on . A unidimensional simple theory eliminates the quantifier ∃∞ and either interprets (in Ceq) an infinite type-definable group or has the property that ACL(Q) = C for every infinite definable set Q.

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50

Wagner, Frank O. "A note on defining groups in stable structures." Journal of Symbolic Logic 59, no. 2 (1994): 575–78. http://dx.doi.org/10.2307/2275408.

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AbstractIf * is a binary partial function which happens to be a group law on some infinite subset of some model of a stable theory, then this subset can be embedded into a definable group such that * becomes the group operation.

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