Results 31 to 40 of about 29,505 (192)
Groups having complete bipartite divisor graphs for their conjugacy class sizes
Rendiconti del Seminario Matematico della Università di Padova, 2015 Given a finite group G , the bipartite divisor graph for its conjugacy class sizes is the bipartite graph with bipartition consisting of the set of conjugacy class sizes of
Hafezieh, R, SPIGA, PABLO
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Finite groups have more conjugacy classes [PDF]
, 2015 We prove that for every $\epsilon > 0$ there exists a $\delta > 0$ so that every group of order $n \geq 3$ has at least $\delta \log_{2} n/{(\log_{2} \log_{2} n)}^{3+\epsilon}$ conjugacy classes. This sharpens earlier results of Pyber and Keller. Bertram
Baumeister, Barbara +2 more
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Character expansiveness in finite groups [PDF]
International Journal of Group Theory, 2013 We say that a finite group $G$ is conjugacy expansive if for anynormal subset $S$ and any conjugacy class $C$ of $G$ the normalset $SC$ consists of at least as many conjugacy classes of $G$ as$S$ does.
Attila Maroti +2 more
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Representations of group rings and groups [PDF]
International Journal of Group Theory, 2018 An isomorphism between the group ring of a finite group and a ring of certain block diagonal matrices is established. It is shown that for any group ring matrix $A$ of $mathbb{C} G$ there exists a matrix $U$ (independent of $A$) such that $U^{-1}AU= diag(
Ted Hurley
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Kazhdan constants for conjugacy classes of compact groups
Journal of Algebra, 2003 Let \(G\) be a locally compact group and \(\pi\) a unitary representation of \(G\) in the Hilbert space of \({\mathcal H}_\pi\). Associated to \(\pi\) and any compact subset \(Q\) of \(G\) is a so-called Kazhdan constant defined by \[ K(\pi,G,Q)= \inf\Biggl\{\sup_{x\in Q}\|\pi(x) \xi- \xi\|:\xi\in{\mathcal H}_\pi,\|\xi\|= 1\Biggr\}. \] Let \(R\) denote
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Integrality, duality and finiteness in combinatoric topological strings
Journal of High Energy Physics, 2022 A remarkable result at the intersection of number theory and group theory states that the order of a finite group G (denoted |G|) is divisible by the dimension d R of any irreducible complex representation of G.
Robert de Mello Koch +3 more
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Decidability and Independence of Conjugacy Problems in Finitely Presented Monoids
, 2017 There have been several attempts to extend the notion of conjugacy from groups to monoids. The aim of this paper is study the decidability and independence of conjugacy problems for three of these notions (which we will denote by $\sim_p$, $\sim_o$, and $
Araújo, João +3 more
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Quasirandom groups enjoy interleaved mixing
Discrete Analysis, 2023 Quasirandom groups enjoy interleaved mixing, Discrete Analysis 2023:14, 4 pp. In 1985 Babai and Sós asked whether there is a constant $c>0$ such that every group of order $n>1$ has a product-free subset of size at least $cn$, where this means a set $A ...
Harm Derksen, Emanuele Viola
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Upper Bounds for the Number of Conjugacy Classes of a Finite Group
Journal of Algebra, 1997 The authors' abstract gives a concise summary: For a finite group \(G\), let \(k(G)\) denote the number of conjugacy classes of \(G\). We prove that a simple group of Lie type of untwisted rank \(l\) over the field of \(q\) elements has at most \((6q)^l\) conjugacy classes. Using this estimate we show that for completely reducible subgroups \(G\) of \(\
Liebeck, Martin W., Pyber, László
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On a group of the form $2^{11}:M_{24}$ [PDF]
AUT Journal of Mathematics and ComputingThe Conway group $Co_{1}$ is one of the $26$ sporadic simple groups. It is the largest of the three Conway groups with order $4157776806543360000=2^{21}.3^9.5^4.7^2.11.13.23$ and has $22$ conjugacy classes of maximal subgroups.
Vasco Mugala +2 more
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