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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
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- 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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