Results 111 to 120 of about 301 (137)

Conjugacy class sizes and solvability of finite groups

Monatshefte Fur Mathematik, 2011
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Qingjun Kong, Kong Qingjun
exaly   +3 more sources

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.
Qingjun Kong, Xiuyun Guo, Kong Qingjun   +2 more
exaly   +4 more sources

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.
Antonio Beltran, Maria JOSÉ Felipe
exaly   +4 more sources

On the Normal Subgroup with Minimal G-Conjugacy Class Sizes

Mediterranean Journal of Mathematics, 2021
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Xianhe Zhao, Chen Ruifang, Zhao Xianhe   +2 more
exaly   +2 more sources

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
exaly   +2 more sources

Frobenius Groups with Almost Distinct Conjugacy Class Sizes

Bulletin of the Malaysian Mathematical Sciences Society, 2016
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Sajjad Mahmood Robati
exaly   +3 more sources

A note on conjugacy class sizes and solvability of finite groups

Monatshefte Fur Mathematik, 2014
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Qingjun Kong, Kong Qingjun
exaly   +3 more sources

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, Kong Qingjun
exaly   +2 more sources

Implications of conjugacy class size

Journal of Group Theory, 1998
Let \(G\) be a finite group. An \(r\)-tuple \(\{n_1,n_2,\ldots,n_r\}\) is said to be the conjugacy type vector of \(G\) if \(n_1>n_2>\cdots>n_r\) are all the numbers that occur as sizes of conjugacy classes of \(G\). Define \(\{n_1,\ldots,n_r\}\times\{m_1,\ldots,m_s\}\) as the set \(\{n_im_j\mid 1\leq i\leq r\), \(1\leq j\leq s\}\).
Camina, A. R., Camina, R. D.
openaire   +2 more sources

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, Felipe Román, María Josefa   +1 more
openaire   +4 more sources