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CONJUGACY CLASS SIZE CONDITIONS WHICH IMPLY SOLVABILITY
Published online by Cambridge University Press: 15 January 2013
Abstract
Let $G$ 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
$n$. Then
$G$ is, up to central factors, a
$\{ p, q\} $-group with
$p$ and
$q$ two distinct primes. In particular,
$G$ is solvable.
MSC classification
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 88 , Issue 2 , October 2013 , pp. 297 - 300
- Copyright
- Copyright ©2012 Australian Mathematical Publishing Association Inc.
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