Results 11 to 20 of about 301 (137)
Conjugacy classes contained in normal subgroups: an overview [PDF]
International Journal of Group Theory, 2018 We survey known results concerning how the conjugacy classes contained in a normal subgroup and their sizes exert an influence on the normal structure of a finite group.
Antonio Beltran +2 more
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On the number of prime divisors of character degrees and conjugacy classes of a finite group
Comptes Rendus. Mathématique, 2022 A result of Gluck is that any finite group $G$ has an abelian subgroup $A$ such that $|G : A|$ is bounded by a polynomial function of the largest irreducible character degree of $G$. Moretó presented a variation of this result that looks at the number of
Yang, Yong
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CONJUGACY CLASS SIZES OF CERTAIN DIRECT PRODUCTS [PDF]
Bulletin of the Australian Mathematical Society, 2012 AbstractWe consider finite groups in which, for all primes p, the p-part of the length of any conjugacy class is trivial or fixed. We obtain a full description in the case in which for each prime divisor p of the order of the group there exists a noncentral conjugacy class of p-power size.
CASOLO, CARLO, E. M. Tombari
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The one-prime power hypothesis for conjugacy classes restricted to normal subgroups and quotient groups [PDF]
International Journal of Group Theory, 2019 We say that a group $G$ satisfies the one-prime power hypothesis for conjugacy classes if the greatest common divisor for all pairs of distinct conjugacy class sizes are prime powers.
Julian Brough
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Finite groups with the same conjugacy class sizes as a finite simple group [PDF]
International Journal of Group Theory, 2019 For a finite group $H$, let $cs(H)$ denote the set of non-trivial conjugacy class sizes of $H$ and $OC(H)$ be the set of the order components of $H$. In this paper, we show that if $S$ is a finite simple group with the disconnected prime graph and $
Neda Ahanjideh
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Conjugacy class sizes in arithmetic progression [PDF]
Journal of Group Theory, 2020 Abstract Let cs ( G )
Bianchi, Mariagrazia +2 more
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Sets of 𝑝-powers as conjugacy class sizes [PDF]
Proceedings of the American Mathematical Society, 1999 We show that any finite set of powers of a fixed prime p p which includes
Cossey, Peter (John), Hawkes, Trevor
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CONJUGACY CLASS SIZE CONDITIONS WHICH IMPLY SOLVABILITY [PDF]
Bulletin of the Australian Mathematical Society, 2013 AbstractLet $G$ be a finite $p$-solvable group and let ${G}^{\ast } $ be the set of elements of primary and biprimary orders of $G$. Suppose that the conjugacy class sizes of ${G}^{\ast } $ are $\{ 1, {p}^{a} , n, {p}^{a} n\} $, where the prime $p$ divides the positive integer $n$ and ${p}^{a} $ does not divide $n$.
Kong, Qingjun, Liu, Qingfeng
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CONJUGACY CLASS SIZES IN FINITE GROUPS [PDF]
Journal of the Australian Mathematical Society, 2008 AbstractWe make several conjectures, and prove some results, pertaining to conjugacy classes of a given size in finite groups, especially in p-groups and 2-groups.
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On groups with conjugacy classes of distinct sizes
Journal of Algebra, 2004 We say that a finite group \(G\) is an ah-group if any two distinct conjugacy classes of \(G\) have different sizes. (The ah-group name comes from the phrase anti-homogeneous.) An ah-group is easily seen to be rational, meaning that all its characters are rational valued. This fact alone greatly restricts the structure of an ah-group.
Arad, Zvi +2 more
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