Results 21 to 30 of about 6,291 (145)
Finite Groups with Four Conjugacy Class Sizes
Communications in Algebra, 2011 We determine the structure of all finite groups with four class sizes when two of them are coprime numbers larger than 1. We prove that such groups are solvable and that the set of class sizes is exactly {1, m, n, mk}, where m, n > 1 are coprime numbers and k > 1 is a divisor of n.
Beltrán, Antonio +1 more
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Detecting the prime divisors of the character degrees and the class sizes by a subgroup generated with few elements [PDF]
, 2018 We prove that every finite group G contains a three-generated subgroup H with the following property: a prime p divides the degree of an irreducible character of G if and only if it divides the degree of an irreducible character of H: There is no ...
Lucchini, Andrea
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Finite groups with real conjugacy classes of prime size [PDF]
Israel Journal of Mathematics, 2010 In this article, the authors establish results characterizing finite groups whose real conjugacy classes are of prime power size. A conjugacy class \(g^G\) is called real if \(g^G=(g^{-1})^G\). These are precisely the conjugacy classes on which every character of \(G\) takes on a real value. In Theorem A, the authors establish that if \(G\) is a finite
DOLFI, SILVIO, L. Sanus, E. Pacifici
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On C-small conjugacy classes in a reductive group [PDF]
, 2010 Let G be an almost simple reductive group with Weyl group W. Let B be a Borel subgroup of G. Let C be an elliptic conjugacy class in W and let w be an element of minimal length of C.
Lusztig, G.
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Simplicity of normal subgroups and conjugacy class sizes
Monatshefte für Mathematik, 2014 Given a finite group G which possesses a non-abelian simple normal subgroup N having exactly four G-class sizes, we prove that N is isomorphic to PSL(2,2a) with a≥2. Thus, we obtain an extension for normal subgroups of the classic N. Itô’s theorem which characterizes those finite simple groups with exactly four class sizes.
Beltrán, Antonio +1 more
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Spectra of phase point operators in odd prime dimensions and the extended Clifford group [PDF]
, 2007 We analyse the role of the Extended Clifford group in classifying the spectra of phase point operators within the framework laid out by Gibbons et al for setting up Wigner distributions on discrete phase spaces based on finite fields.
D. M. Appleby +4 more
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On the commuting probability and supersolvability of finite groups [PDF]
, 2013 For a finite group $G$, let $d(G)$ denote the probability that a randomly chosen pair of elements of $G$ commute. We prove that if $d(G)>1/s$ for some integer $s>1$ and $G$ splits over an abelian normal nontrivial subgroup $N$, then $G$ has a nontrivial ...
Lescot, Paul +2 more
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Groups with reality and conjugacy conditions [PDF]
International Journal of Group Theory, 2012 Many results were proved on the structure of finite groups with some restrictions on their real elements and on their conjugacy classes. We generalize a few of these to some classes of infinite groups.
Patrizia Longobardi +2 more
doaj
Conjugacy class sizes and solvability of finite groups
Proceedings - Mathematical Sciences, 2013 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jiang, Qinhui, Shao, Changguo
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Derived length and conjugacy class sizes
Advances in Mathematics, 2006 Let \(G\) be a finite solvable group, let \(F(G)\) denote the Fitting subgroup and let \(\text{dl}(G/F(G))\) stand for the derived length of \(G/F(G)\). If \(\text{cs}(G)\) is the set of conjugacy class sizes of \(G\) and if \(\text{h}(G)\) is the Fitting height of \(G\), the author succeeds to prove (Theorem A) that there exist universal constants ...
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