Relevant bibliographies by topics / Infinite groups : Group theory

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
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Academic literature on the topic 'Infinite groups : Group theory'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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

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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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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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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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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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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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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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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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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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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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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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Dissertations / Theses on the topic "Infinite groups : Group theory"

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Griffin, Cornelius John. "Subgroups of infinite groups : interactions between group theory and number theory." Thesis, University of Nottingham, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.252018.

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Wharton, Elizabeth. "The model theory of certain infinite soluble groups." Thesis, University of Oxford, 2006. http://ora.ox.ac.uk/objects/uuid:7bd8d05b-4ff6-4326-8463-f896e2862e25.

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This thesis is concerned with aspects of the model theory of infinite soluble groups. The results proved lie on the border between group theory and model theory: the questions asked are of a model-theoretic nature but the techniques used are mainly group-theoretic in character. We present a characterization of those groups contained in the universal closure of a restricted wreath product U wr G, where U is an abelian group of zero or finite square-free exponent and G is a torsion-free soluble group with a bound on the class of its nilpotent subgroups. For certain choices of G we are able to us
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Ramsay, Denise. "On linearly ordered sets and permutation groups of uncountable degree." Thesis, University of Oxford, 1990. http://ora.ox.ac.uk/objects/uuid:ce9a8b26-bb4c-4c85-8231-78e89ce4109d.

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In this thesis a set, Ω, of cardinality N<sub>K</sub> and a group acting on Ω, with N<sub>K+1</sub> orbits on the power set of Ω, is found for every infinite cardinal N<sub>K</sub>. Let W<sub>K</sub> denote the initial ordinal of cardinality N<sub>K</sub>. Define N := {α<sub>1</sub>α<sub>2</sub> . . . α<sub>n</sub>∣ 0 < n < w, α<sub>j</sub> ∈ w<sub>K</sub> for j = 1, . . .,n, α<sub>n</sub> a successor ordinal} R := {ϰ ∈ N ∣ length(ϰ) = 1 mod 2} and let these sets be ordered lexicographically. The order types of N and R are Κ-types (countable unions of scattered types) which have cardinality N<
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Smith, Simon Mark. "Subdegree growth rates of infinite primitive permutation groups." Thesis, University of Oxford, 2005. http://ora.ox.ac.uk/objects/uuid:1baa0e15-363a-4163-b21b-59fcd62d210b.

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If G is a group acting on a set Ω, and α, β ∈ Ω, the directed graph whose vertex set is Ω and whose edge set is the orbit (α, β)<sup>G</sup> is called an orbital graph of G. These graphs have many uses in permutation group theory. A graph Γ is said to be primitive if its automorphism group acts primitively on its vertex set, and is said to have connectivity one if there is a vertex α such that the graph Γ\{α} is not connected. A half-line in Γ is a one-way infinite path in Γ. The ends of a locally finite graph Γ are equivalence classes on the set of half-lines: two half-lines lie in the same e
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Riley, Timothy Rupert. "Asymptotic invariants of infinite discrete groups." Thesis, University of Oxford, 2002. http://ora.ox.ac.uk/objects/uuid:30f42f4c-e592-44c2-9954-7d9e8c1f3d13.

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<b>Asymptotic cones.</b> A finitely generated group has a word metric, which one can scale and thereby view the group from increasingly distant vantage points. The group coalesces to an "asymptotic cone" in the limit (this is made precise using techniques of non-standard analysis). The reward is that in place of the discrete group one has a continuous object "that is amenable to attack by geometric (e.g. topological, infinitesimal) machinery" (to quote Gromov). We give coarse geometric conditions for a metric space X to have N-connected asymptotic cones. These conditions are expressed in terms
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Bernstein, Brett David. "Higher natural numbers and omega words." Diss., Online access via UMI:, 2005.

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Hume, David S. "Embeddings of infinite groups into Banach spaces." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:e38f58ec-484c-4088-bb44-1556bc647cde.

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In this thesis we build on the theory concerning the metric geometry of relatively hyperbolic and mapping class groups, especially with respect to the difficulty of embedding such groups into Banach spaces. In Chapter 3 (joint with Alessandro Sisto) we construct simple embeddings of closed graph manifold groups into a product of three metric trees, answering positively a conjecture of Smirnov concerning the Assouad-Nagata dimension of such spaces. Consequently, we obtain optimal embeddings of such spaces into certain Banach spaces. The ideas here have been extended to other closed three-manifo
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Olukoya, Feyisayo. "Decision problems in groups of homeomorphisms of Cantor space." Thesis, University of St Andrews, 2018. http://hdl.handle.net/10023/15885.

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The Thompson groups $F, T$ and $V$ are important groups in geometric group theory: $T$ and $V$ being the first discovered examples of finitely presented infinite simple groups. There are many generalisations of these groups including, for $n$ and $r$ natural numbers and $1 < r < n$, the groups $F_{n}$, $T_{n,r}$ and $G_{n,r}$ ($T ≅ T_{2,1}$ and $V ≅ G_{2,1}$). Automorphisms of $F$ and $T$ were characterised in the seminal paper of Brin ([16]) and, later on, Brin and Guzman ([17]) investigate automorphisms of $T_{n, n-1}$ and $F_{n}$ for $n > 2$. However, their techniques give no information ab
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Ramras, Daniel A. "Stable representation theory of infinite discrete groups /." May be available electronically:, 2007. http://proquest.umi.com/login?COPT=REJTPTU1MTUmSU5UPTAmVkVSPTI=&clientId=12498.

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Carruth, Nathan Thomas. "Classical Foundations for a Quantum Theory of Time in a Two-Dimensional Spacetime." DigitalCommons@USU, 2010. https://digitalcommons.usu.edu/etd/708.

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We consider the set of all spacelike embeddings of the circle S1 into a spacetime R1 × S1 with a metric globally conformal to the Minkowski metric. We identify this set and the group of conformal isometries of this spacetime as quotients of semidirect products involving diffeomorphism groups and give a transitive action of the conformal group on the set of spacelike embeddings. We provide results showing that the group of conformal isometries is a topological group and that its action on the set of spacelike embeddings is continuous. Finally, we point out some directions for future research.
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Books on the topic "Infinite groups : Group theory"

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Groups, graphs, and trees: An introduction to the geometry of infinite groups. Cambridge University Press, 2008.

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Meier, John. Groups, graphs, and trees: An introduction to the geometry of infinite groups. Cambridge University Press, 2008.

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Ismagilov, R. S. Representations of infinite-dimensional groups. American Mathematical Society, 1996.

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AMS Special Session in Combinatorial Group Theory--Infinite Groups (1988 University of Maryland, College Park). Combinatorial group theory: Proceedings of the AMS special session in combinatorial group theory-infinite groups, April 23-24, 1988. Edited by Fine Benjamin 1948-, Gaglione Anthony M, Tang, Francis C. Y., 1935-, and American Mathematical Society. American Mathematical Society, 1990.

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Alexandre, Borovik, ed. Groups, languages, algorithms: AMS-ASL Joint Special Session on Interactions between Logic, Group Theory, and Computer Science, January 16-19, 2003, Baltimore, Maryland. American Mathematical Society, 2005.

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Amberg, Bernhard. Products of groups. Clarendon Press, 1992.

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Bestvina, Mladen, Michah Sageev, and Karen Vogtmann. Geometric group theory. American Mathematical Society, 2014.

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Potential theory on infinite-dimensional Abelian groups. Walter de Gruyter, 1995.

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Representation theory of infinite groups and finite quasigroups. Presses de l'Université de Montréal, 1986.

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Gerhard, Rosenberger, Fine Benjamin 1948-, Gaglione Anthony M, and Spellman Dennis 1945-, eds. Combinatorial group theory, discrete groups, and number theory: A conference in honor of Gerhard Rosenberger, December 8-9, 2004, Fairfield University : AMS Special Session on Infinite Groups, October 8-9, 2005, Bard College. American Mathematical Society, 2006.

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Book chapters on the topic "Infinite groups : Group theory"

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Bhattacharjee, Meenaxi, Rögnvaldur G. Möller, Dugald Macpherson, and Peter M. Neumann. "Some Group Theory." In Notes on Infinite Permutation Groups. Hindustan Book Agency, 1997. http://dx.doi.org/10.1007/978-93-80250-91-5_1.

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Dehn, Max. "On Infinite Discontinuous Groups." In Papers on Group Theory and Topology. Springer New York, 1987. http://dx.doi.org/10.1007/978-1-4612-4668-8_8.

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Méliot, Pierre-Loïc. "Representations of the infinite symmetric group." In Representation Theory of Symmetric Groups. Chapman and Hall/CRC, 2017. http://dx.doi.org/10.1201/9781315371016-15.

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Robinson, Derek J. S. "Infinite Soluble Groups." In A Course in the Theory of Groups. Springer US, 1993. http://dx.doi.org/10.1007/978-1-4684-0128-8_15.

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Robinson, Derek J. S. "Infinite Soluble Groups." In A Course in the Theory of Groups. Springer New York, 1996. http://dx.doi.org/10.1007/978-1-4419-8594-1_15.

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Cai, Jin-yi. "Computations over infinite groups." In Fundamentals of Computation Theory. Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/3-540-54458-5_46.

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Berrick, A. J., and P. H. Kropholler. "Groups with infinite homology." In Cohomological Methods in Homotopy Theory. Birkhäuser Basel, 2001. http://dx.doi.org/10.1007/978-3-0348-8312-2_4.

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McCleary, Stephen H. "Lattice-ordered Permutation Groups: The Structure Theory." In Ordered Groups and Infinite Permutation Groups. Springer US, 1996. http://dx.doi.org/10.1007/978-1-4613-3443-9_2.

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Baumslag, Gilbert, and Peter B. Shalen. "Affine Algebraic Sets and Some Infinite Finitely Presented Groups." In Essays in Group Theory. Springer New York, 1987. http://dx.doi.org/10.1007/978-1-4613-9586-7_1.

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Nathanson, Melvyn B. "Not All Groups Are LEF Groups, or Can You Know If a Group Is Infinite?" In Combinatorial and Additive Number Theory III. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-31106-3_13.

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Conference papers on the topic "Infinite groups : Group theory"

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SCHMID, RUDOLF. "THE LIE GROUP OF FOURIER INTEGRAL OPERATORS ON OPEN MANIFOLDS." In Infinite Dimensional Lie Groups in Geometry and Representation Theory. WORLD SCIENTIFIC, 2002. http://dx.doi.org/10.1142/9789812777089_0004.

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BORZELLINO, JOSEPH E., and VICTOR BRUNSDEN. "ORBIFOLD HOMEOMORPHISM AND DIFFEOMORPHISM GROUPS." In Infinite Dimensional Lie Groups in Geometry and Representation Theory. WORLD SCIENTIFIC, 2002. http://dx.doi.org/10.1142/9789812777089_0009.

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TEICHMANN, JOSEF. "INHERITANCE PROPERTIES FOR LIPSCHITZ-METRIZABLE FRÖLICHER GROUPS." In Infinite Dimensional Lie Groups in Geometry and Representation Theory. WORLD SCIENTIFIC, 2002. http://dx.doi.org/10.1142/9789812777089_0001.

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PESTOV, VLADIMIR. "REMARKS ON ACTIONS ON COMPACTA BY SOME INFINITE-DIMENSIONAL GROUPS." In Infinite Dimensional Lie Groups in Geometry and Representation Theory. WORLD SCIENTIFIC, 2002. http://dx.doi.org/10.1142/9789812777089_0011.

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ROBART, THIERRY. "AROUND THE EXPONENTIAL MAPPING." In Infinite Dimensional Lie Groups in Geometry and Representation Theory. WORLD SCIENTIFIC, 2002. http://dx.doi.org/10.1142/9789812777089_0002.

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LESLIE, JOSHUA A. "ON A SOLUTION TO A GLOBAL INVERSE PROBLEM WITH RESPECT TO CERTAIN GENERALIZED SYMMETRIZABLE KAC-MOODY ALGEBRAS." In Infinite Dimensional Lie Groups in Geometry and Representation Theory. WORLD SCIENTIFIC, 2002. http://dx.doi.org/10.1142/9789812777089_0003.

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WADE, AISSA. "ON SOME PROPERTIES OF LEIBNIZ ALGEBROIDS." In Infinite Dimensional Lie Groups in Geometry and Representation Theory. WORLD SCIENTIFIC, 2002. http://dx.doi.org/10.1142/9789812777089_0005.

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BANYAGA, A. "ON THE GEOMETRY OF LOCALLY CONFORMAL SYMPLECTIC MANIFOLDS." In Infinite Dimensional Lie Groups in Geometry and Representation Theory. WORLD SCIENTIFIC, 2002. http://dx.doi.org/10.1142/9789812777089_0006.

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HALLER, STEFAN. "SOME PROPERTIES OF LOCALLY CONFORMAL SYMPLECTIC MANIFOLDS." In Infinite Dimensional Lie Groups in Geometry and Representation Theory. WORLD SCIENTIFIC, 2002. http://dx.doi.org/10.1142/9789812777089_0007.

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RUKIMBIRA, PHILIPPE. "CRITICALITY OF UNIT CONTACT VECTOR FIELDS." In Infinite Dimensional Lie Groups in Geometry and Representation Theory. WORLD SCIENTIFIC, 2002. http://dx.doi.org/10.1142/9789812777089_0008.

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Reports on the topic "Infinite groups : Group theory"

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Glockner, Helge. Fundamental Problems in the Theory of Infinite-Dimensional Lie Groups. Journal of Geometry and Symmetry in Physics, 2012. http://dx.doi.org/10.7546/jgsp-5-2006-24-35.

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