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SOLVABILITY OF FINITE GROUPS WITH FOUR CONJUGACY CLASS SIZES OF CERTAIN ELEMENTS

Part of: Structure and classification of infinite or finite groups Representation theory of groups

Published online by Cambridge University Press:  21 July 2014

QINHUI JIANG  and
CHANGGUO SHAO
QINHUI JIANG
Affiliation:
School of Mathematical Sciences, University of Jinan, Shandong, 250022, PR China email syjqh2001@163.com
CHANGGUO SHAO*
Affiliation:
School of Mathematical Sciences, University of Jinan, Shandong, 250022, PR China email shaoguozi@163.com
*
✉shaoguozi@163.com
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Abstract

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Assume that $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}m$ and $n$ are two positive integers which do not divide each other. If the set of conjugacy class sizes of primary and biprimary elements of a group $G$ is $\{1, m, n, mn\}$, we show that up to central factors $G$ is a $\{p,q\}$-group for two distinct primes $p$ and $q$.

Keywords

conjugacy class sizesprimary and biprimary elementsfinite groups

MSC classification

Secondary: 20E45: Conjugacy classes 20D10: Solvable groups, theory of formations, Schunck classes, Fitting classes, $pi$-length, ranks
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 90 , Issue 2 , October 2014 , pp. 250 - 256
Copyright
Copyright © 2014 Australian Mathematical Publishing Association Inc. 

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