Results 131 to 140 of about 6,291 (145)

Conjugacy class sizes and solvability of finite groups

Monatshefte für Mathematik, 2011
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ON -PARTS OF CONJUGACY CLASS SIZES OF FINITE GROUPS

Bulletin of the Australian Mathematical Society, 2018
Let $G$ be a finite group. Let $\operatorname{cl}(G)$ be the set of conjugacy classes of $G$ and let $\operatorname{ecl}_{p}(G)$ be the largest integer such that $p^{\operatorname{ecl}_{p}(G)}$ divides $|C|$ for some $C\in \operatorname{cl}(G)$. We prove the following results. If $\operatorname{ecl}_{p}(G)=1$, then $|G:F(G)|_{p}\leq p^{4}$ if $p\geq 3$.
YONG YANG, GUOHUA QIAN
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ON THE THOMPSON'S CONJECTURE ON CONJUGACY CLASSES SIZES

International Journal of Algebra and Computation, 2013
In this paper, we prove a conjecture of Thompson for an infinite class of simple groups of Lie type. In fact, we show that every finite group G with the property Φ(G) ∩ Z(G) = 1 and N(G) = N(Dn(q)) is isomorphic to Z(G) × Dn(q), where n ≥ 5 and n ≠ 8. Note that N(G), Φ(G) and Z(G) are the set of lengths of conjugacy classes of G, Frattini subgroup of ...
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On an extension of a theorem on conjugacy class sizes

Israel Journal of Mathematics, 2010
The authors generalise a result of the reviewer in 1972 [J. Lond. Math. Soc., II. Ser. 5, 127-132 (1972; Zbl 0242.20025)] in which it was proved that if the conjugacy classes of a finite group have sizes precisely \(\{1,p^a,q^b,p^aq^b\}\) where \(p^a\) and \(q^b\) are prime powers then the group is nilpotent. Later \textit{A. Beltrán} and \textit{M. J.
Kong, Qingjun, Guo, Xiuyun
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ON CONJUGACY CLASS SIZES AND CHARACTER DEGREES OF FINITE GROUPS

Journal of Algebra and Its Applications, 2013
Let p be a fixed prime, G a finite group and P a Sylow p-subgroup of G. The main results of this paper are as follows: (1) If gcd (p-1, |G|) = 1 and p2 does not divide |xG| for any p′-element x of prime power order, then G is a solvable p-nilpotent group and a Sylow p-subgroup of G/Op(G) is elementary abelian. (2) Suppose that G is p-solvable. If pp-
Qian, Guohua, Wang, Yanming
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A note on conjugacy class sizes of finite groups

Mathematical Notes, 2009
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On coprime G-conjugacy class sizes in a normal subgroup

Acta Mathematica Sinica, English Series, 2014
The set of conjugacy class sizes of a finite group \(G\) exerts a strong influence on the structure of \(G\), and in the past few years, it has been put forward that the sizes of the conjugacy classes of \(G\) contained in a normal subgroup \(N\) of \(G\) can also have a strong control on the structure of \(N\). In 1981, L. Kazarin showed that when the
Zhao, Xian He, Qu, Hai Peng, Chen, Gui Yun   +2 more
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Determining group structure by set of conjugacy class sizes

Communications in Algebra, 2019
Let G be a finite group. Let further m1,m2,m3 be three positive integers such that m1 and m2 do not divide each other and m1m2 is coprime to m3.
Changguo Shao, Qinhui Jiang
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A note on conjugacy class sizes of finite groups.

2001
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M. Bianchi, A. Gillio, C. Casolo
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A note on a theorem on conjugacy class sizes

Ricerche di Matematica
Let \(G\) be a finite group and \(p\) a fixed prime. Assume that for every prime \(q\), the set of conjugacy class sizes of all \(\{p,q\}\)-elements in \(G\) is \(\{1, p^a, n, p^a n\}\), with \((p,n) = 1\) and that there exists a \(p\)-element in \(G\) whose conjugacy class has size \(p^a\).
Qingjun Kong, Mengjiao Shi
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