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SOLVABILITY OF FINITE GROUPS WITH FOUR CONJUGACY CLASS SIZES OF CERTAIN ELEMENTS
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 90 / Issue 2 / October 2014
- Published online by Cambridge University Press:
- 21 July 2014, pp. 250-256
- Print publication:
- October 2014
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- Article
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- You have access
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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 
$q$.
