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SOLVABILITY OF FINITE GROUPS WITH FOUR CONJUGACY CLASS SIZES OF CERTAIN ELEMENTS
Published online by Cambridge University Press: 21 July 2014
Abstract
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 $q$.
MSC classification
- 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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