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Conjugacy Class Sizes in Affine Semi-linear Groups [PDF]
Advances in Group Theory and Applications, 2020 The aim of this work is to study the structure and sizes of conjugacy classes in certain affine semi-linear groups. This provides a wealth of finite groups of small conjugate rank that are solvable and non-nilpotent.
Hossein Shahrtash
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One-prime power hypothesis for conjugacy class sizes [PDF]
International Journal of Group Theory, 2017 A finite group $G$ satisfies the on-prime power hypothesis for conjugacy class sizes if any two conjugacy class sizes $m$ and $n$ are either equal or have a common divisor a prime power. Taeri conjectured that an insoluble group satisfying this condition
Alan Camina, Rachel Camina
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On finite groups with square-free conjugacy class sizes [PDF]
International Journal of Group Theory, 2018 We report on finite groups having square-free conjugacy class sizes, in particular in the framework of factorised groups.
Maria-Jose Felipe +2 more
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Restrictions on sets of conjugacy class sizes in arithmetic progressions [PDF]
International Journal of Group Theory, 2023 We continue the investigation, that began in [M. Bianchi, A. Gillio and P. P. Pálfy, A note on finite groups in which the conjugacy class sizes form an arithmetic progression, Ischia group theory 2010, World Sci. Publ., Hackensack, NJ (2012) 20--25.] and
Alan R. Camina, Rachel D. Camina
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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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COPRIME CONJUGACY CLASS SIZES [PDF]
Asian-European Journal of Mathematics, 2009 We consider finite groups in which every triple of distinct conjugacy class sizes greater than one has a pair which is coprime. We prove such a group is soluble and has conjugate rank at most three.
Camina, A. R., Camina, R. D.
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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 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 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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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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