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Journal articles on the topic 'Finite products'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Diaz, Francisco Diaz y., and Eduardo Friedman. "Finite products of regularized products." Mathematical Research Letters 15, no. 1 (2008): 33–41. http://dx.doi.org/10.4310/mrl.2008.v15.n1.a3.

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2

Nicolau, Artur. "Finite Products of Interpolating Blaschke Products." Journal of the London Mathematical Society 50, no. 3 (1994): 520–31. http://dx.doi.org/10.1112/jlms/50.3.520.

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3

ARTEAGA, CARLOS. "Commuting finite Blaschke products." Ergodic Theory and Dynamical Systems 19, no. 3 (1999): 549–52. http://dx.doi.org/10.1017/s0143385799130165.

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We consider the set of finite Blaschke products $F$ for which the fixed points on the circle $S^1$ are expanding and we prove that if $F'(x) \ne F'(y)$ for all different fixed points $x,y$ of $F$ on $S^1$, then $F$ commutes only with its own powers.

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4

Daepp, Ulrich, Pamela Gorkin, Andrew Shaffer, Benjamin Sokolowsky, and Karl Voss. "Decomposing finite Blaschke products." Journal of Mathematical Analysis and Applications 426, no. 2 (2015): 1201–16. http://dx.doi.org/10.1016/j.jmaa.2015.01.039.

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5

Brewster, Ben, and Elizabeth Wilcox. "Complete finite semidirect products and wreath products." Archiv der Mathematik 96, no. 4 (2011): 301–9. http://dx.doi.org/10.1007/s00013-011-0237-2.

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6

Marín, Víctor, and Héctor Pinedo. "Groupoids: Direct products, semidirect products and solvability." Algebra and Discrete Mathematics 33, no. 2 (2022): 92–107. http://dx.doi.org/10.12958/adm1772.

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We present some constructions of groupoids such as: direct product, semidirect product and give necessary and sufficient conditions for a groupoid to be embedded into a direct product of groupoids. Also, we establish necessary and sufficient conditions to determine when a semidirect product is direct. Finally the notion of solvable groupoid is introduced and studied, in particular it is shown that a finite groupoid G is solvable if and only if its isotropy groups are.

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7

Corona-Vázquez, Florencio, Russell Aarón Quiñones-Estrella, Javier Sánchez-Martínez, and Hugo Villanueva. "Embedding products into symmetric products of finite graphs." Topology and its Applications 241 (June 2018): 162–71. http://dx.doi.org/10.1016/j.topol.2018.04.003.

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8

Imam, A. T., and M. J. Ibrahim. "On products of 3-paths in finite full transformation semigroups." Algebra and Discrete Mathematics 33, no. 2 (2022): 60–77. http://dx.doi.org/10.12958/adm1770.

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Let Singn denotes the semigroup of all singular self-maps of a finite set Xn={1,2, . . . , n}. A map α∈Singn is called a 3-path if there are i, j, k∈Xn such that iα=j,jα=k and xα=x for all x∈Xn\ {i, j}. In this paper, we described aprocedure to factorise each α∈Singn into a product of 3-paths. The length of each factorisation, that is the number of factors in eachfactorisation, is obtained to be equal to ⌈12(g(α)+m(α))⌉, where g(α) is known as the gravity of α and m(α) is a parameter introduced inthis work and referred to as the measure of α. Moreover, we showed that Singn⊆P[n−1], where P deno

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9

Daepp, Ulrich, Pamela Gorkin, and Raymond Mortini. "Ellipses and Finite Blaschke Products." American Mathematical Monthly 109, no. 9 (2002): 785. http://dx.doi.org/10.2307/3072367.

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10

Gállego, María Pilar, Peter Hauck, Lev S. Kazarin, Ana Martínez-Pastor, and María Dolores Pérez-Ramos. "Products of Finite Connected Subgroups." Mathematics 8, no. 9 (2020): 1498. http://dx.doi.org/10.3390/math8091498.

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For a non-empty class of groups L, a finite group G=AB is said to be an L-connected product of the subgroups A and B if ⟨a,b⟩∈L for all a∈A and b∈B. In a previous paper, we prove that, for such a product, when L=S is the class of finite soluble groups, then [A,B] is soluble. This generalizes the theorem of Thompson that states the solubility of finite groups whose two-generated subgroups are soluble. In the present paper, our result is applied to extend to finite groups previous research about finite groups in the soluble universe. In particular, we characterize connected products for relevant

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11

Liu, Xi, Wenbin Guo, and K. P. Shum. "Products of Finite Supersoluble Groups." Algebra Colloquium 16, no. 02 (2009): 333–40. http://dx.doi.org/10.1142/s1005386709000327.

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Let H and T be subgroups of a finite group G. We say that H is completely c-permutable with T in G if there exists an element x ∈ 〈H,T〉 such that HTx = TxH. In this paper, we use this concept to determine the supersolubility of a group G = AB, where A and B are supersoluble subgroups of G. Some criterions of supersolubility of such groups are obtained and some known results are generalized.

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12

Cossey, John, and Stewart E. Stonehewer. "Products of finite nilpotent groups." Communications in Algebra 27, no. 1 (1999): 289–300. http://dx.doi.org/10.1080/00927879908826432.

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13

Gau, Hwa-Long, and Pei Yuan Wu. "Finite Blaschke products of contractions." Linear Algebra and its Applications 368 (July 2003): 359–70. http://dx.doi.org/10.1016/s0024-3795(02)00697-3.

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14

Arteaga, Carlos. "Centralizers of finite Blaschke products." Boletim da Sociedade Brasileira de Matem�tica 31, no. 2 (2000): 163–73. http://dx.doi.org/10.1007/bf01244242.

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15

Daepp, Ulrich, Pamela Gorkin, and Raymond Mortini. "Ellipses and Finite Blaschke Products." American Mathematical Monthly 109, no. 9 (2002): 785–95. http://dx.doi.org/10.1080/00029890.2002.11919914.

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16

Heineken, Hermann. "Products of finite nilpotent groups." Mathematische Annalen 287, no. 1 (1990): 643–52. http://dx.doi.org/10.1007/bf01446920.

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17

Agore, A. L., A. Chirvăsitu, B. Ion, and G. Militaru. "Bicrossed Products for Finite Groups." Algebras and Representation Theory 12, no. 2-5 (2009): 481–88. http://dx.doi.org/10.1007/s10468-009-9145-6.

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18

Collins, Benoit, and Pierre Yves Gaudreau Lamarre. "⁎-freeness in finite tensor products." Advances in Applied Mathematics 83 (February 2017): 47–80. http://dx.doi.org/10.1016/j.aam.2016.09.002.

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19

Shirvani, M. "On residually finite graph products." Journal of Pure and Applied Algebra 49, no. 3 (1987): 281–82. http://dx.doi.org/10.1016/0022-4049(87)90136-8.

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20

Birch, Leah M., Jeremy J. Thibodeaux, and Ralph P. Tucci. "Zero Divisor Graphs of Finite Direct Products of Finite Rings." Communications in Algebra 42, no. 9 (2014): 3852–60. http://dx.doi.org/10.1080/00927872.2013.796556.

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21

Martínez, Juan Carlos. "On finite unions and finite products with the D-property." Topology and its Applications 158, no. 2 (2011): 223–28. http://dx.doi.org/10.1016/j.topol.2010.10.017.

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22

Klyachko, A. A., and A. K. Mongush. "Residually finite algorithmically finite groups, their subgroups and direct products." Mathematical Notes 98, no. 3-4 (2015): 414–18. http://dx.doi.org/10.1134/s0001434615090060.

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23

Lee, Young Joo. "Finite sums of dual Toeplitz products." Studia Mathematica 256, no. 2 (2021): 197–215. http://dx.doi.org/10.4064/sm190724-17-12.

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24

Hijazi, Rola A. "Mutually Permutable Products of Finite Groups." ISRN Algebra 2011 (September 7, 2011): 1–4. http://dx.doi.org/10.5402/2011/867082.

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Let G be a finite group and G1, G2 are two subgroups of G. We say that G1 and G2 are mutually permutable if G1 is permutable with every subgroup of G2 and G2 is permutable with every subgroup of G1. We prove that if is the product of three supersolvable subgroups G1, G2, and G3, where Gi and Gj are mutually permutable for all i and j with and the Sylow subgroups of G are abelian, then G is supersolvable. As a corollary of this result, we also prove that if G possesses three supersolvable subgroups whose indices are pairwise relatively prime, and Gi and Gj are mutually permutable for all i and

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25

Dubinin, V. N. "Critical Values of Finite Blaschke Products." Doklady Mathematics 104, no. 1 (2021): 163–64. http://dx.doi.org/10.1134/s1064562421040050.

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26

Wong, Kok-Bin, and Peng-Choon Wong. "POLYGONAL PRODUCTS OF RESIDUALLY FINITE GROUPS." Bulletin of the Korean Mathematical Society 44, no. 1 (2007): 61–71. http://dx.doi.org/10.4134/bkms.2007.44.1.061.

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27

Craighead, R. L., and F. W. Carroll. "A decomposition of finite blaschke products." Complex Variables, Theory and Application: An International Journal 26, no. 4 (1995): 333–41. http://dx.doi.org/10.1080/17476939508814794.

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28

Gonek, S. M., and J. P. Keating. "Mean values of finite Euler products." Journal of the London Mathematical Society 82, no. 3 (2010): 763–86. http://dx.doi.org/10.1112/jlms/jdq049.

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29

Ballester-Bolinches, A., John Cossey, and M. C. Pedraza-Aguilera. "ON PRODUCTS OF FINITE SUPERSOLUBLE GROUPS." Communications in Algebra 29, no. 7 (2001): 3145–52. http://dx.doi.org/10.1081/agb-5013.

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30

Saxl, Jan, Saharon Shelah, and Simon Thomas. "Infinite products of finite simple groups." Transactions of the American Mathematical Society 348, no. 11 (1996): 4611–41. http://dx.doi.org/10.1090/s0002-9947-96-01746-1.

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31

Chalendar, Isabelle, and Raymond Mortini. "When do finite Blaschke products commute?" Bulletin of the Australian Mathematical Society 64, no. 2 (2001): 189–200. http://dx.doi.org/10.1017/s0004972700039861.

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We study the following questions. Which finite Blaschke products are eigenvectors of the composition operatorsTu:f↦f∘u, what are the possible eigenvalues, and which pairs (B,C) of finite Blaschke products commute (that is, satisfyB∘C=C∘B).

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32

Malik, D. S., John N. Mordeson, and M. K. Sen. "Products of fuzzy finite state machines." Fuzzy Sets and Systems 92, no. 1 (1997): 95–102. http://dx.doi.org/10.1016/s0165-0114(96)00166-2.

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33

Castañeda, Enrique, and Alejandro Illanes. "Finite graphs have unique symmetric products." Topology and its Applications 153, no. 9 (2006): 1434–50. http://dx.doi.org/10.1016/j.topol.2005.04.006.

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34

KERR, DAVID, and PIOTR W. NOWAK. "Residually finite actions and crossed products." Ergodic Theory and Dynamical Systems 32, no. 5 (2011): 1585–614. http://dx.doi.org/10.1017/s0143385711000575.

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AbstractWe study a notion of residual finiteness for continuous actions of discrete groups on compact Hausdorff spaces and how it relates to the existence of norm microstates for the reduced crossed product. Our main result asserts that an action of a free group on a zero-dimensional compact metrizable space is residually finite if and only if its reduced crossed product admits norm microstates, i.e., is an MF algebra.

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35

Yang, Jiang, and Xiongwei Zhang. "Finite direct products of EQ-algebras." Soft Computing 23, no. 17 (2018): 7495–504. http://dx.doi.org/10.1007/s00500-018-03687-5.

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36

Swaenepoel, Cathy. "Trace of products in finite fields." Finite Fields and Their Applications 51 (May 2018): 93–129. http://dx.doi.org/10.1016/j.ffa.2018.01.005.

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37

Kirtland, Joseph. "Direct products of inseparable finite groups." Archiv der Mathematik 62, no. 4 (1994): 289–91. http://dx.doi.org/10.1007/bf01201778.

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38

Lin, James P. "Cup products and finite loop spaces." Topology and its Applications 45, no. 1 (1992): 73–84. http://dx.doi.org/10.1016/0166-8641(92)90063-6.

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39

Haglund, Frédéric. "Finite index subgroups of graph products." Geometriae Dedicata 135, no. 1 (2008): 167–209. http://dx.doi.org/10.1007/s10711-008-9270-0.

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40

Karazeris, Panagis, and Grigoris Protsonis. "Left Kan extensions preserving finite products." Journal of Pure and Applied Algebra 216, no. 8-9 (2012): 2014–28. http://dx.doi.org/10.1016/j.jpaa.2012.02.038.

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41

Martínez-Pérez, Conchita. "Finite presentability of normal fibre products." Journal of Pure and Applied Algebra 218, no. 8 (2014): 1373–84. http://dx.doi.org/10.1016/j.jpaa.2013.11.022.

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42

Amberg, Bernhard, and Lev S. Kazarin. "On finite products of soluble groups." Israel Journal of Mathematics 106, no. 1 (1998): 93–108. http://dx.doi.org/10.1007/bf02773462.

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43

Bondarenko, Ievgen V. "Finite generation of iterated wreath products." Archiv der Mathematik 95, no. 4 (2010): 301–8. http://dx.doi.org/10.1007/s00013-010-0169-2.

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44

Amberg, Bernhard, and Burkhard H�fling. "On finite products of nilpotent groups." Archiv der Mathematik 63, no. 1 (1994): 1–8. http://dx.doi.org/10.1007/bf01196291.

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45

Amberg, Bernhard. "Products of groups with finite rank." Archiv der Mathematik 49, no. 5 (1987): 369–75. http://dx.doi.org/10.1007/bf01194092.

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46

Ballester-Bolinches, A., M. D. Pérez-Ramos, and M. C. Pedraza-Aguilera. "Mutually Permutable Products of Finite Groups." Journal of Algebra 213, no. 1 (1999): 369–77. http://dx.doi.org/10.1006/jabr.1998.7653.

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47

Müller, Thomas. "Enumerating Representations in Finite Wreath Products." Advances in Mathematics 153, no. 1 (2000): 118–54. http://dx.doi.org/10.1006/aima.1998.1885.

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48

Gorkin, Pamela, and Robert C. Rhoades. "Boundary Interpolation by Finite Blaschke Products." Constructive Approximation 27, no. 1 (2006): 75–98. http://dx.doi.org/10.1007/s00365-006-0646-3.

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49

Ballester-Bolinches, A., Clara Calvo, and R. Esteban-Romero. "Products of formations of finite groups." Journal of Algebra 299, no. 2 (2006): 602–15. http://dx.doi.org/10.1016/j.jalgebra.2006.01.003.

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50

Arai, Kenichi, Hiroyuki Okazaki, and Yasunari Shidama. "Isomorphisms of Direct Products of Finite Cyclic Groups." Formalized Mathematics 20, no. 4 (2012): 343–47. http://dx.doi.org/10.2478/v10037-012-0038-5.

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Summary In this article, we formalize that every finite cyclic group is isomorphic to a direct product of finite cyclic groups which orders are relative prime. This theorem is closely related to the Chinese Remainder theorem ([18]) and is a useful lemma to prove the basis theorem for finite abelian groups and the fundamental theorem of finite abelian groups. Moreover, we formalize some facts about the product of a finite sequence of abelian groups.

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