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An extension of a theorem of Ito on conjugacy class sizes
International Journal of Statistics and Applied Mathematics · 2017 · Vol. 2(1) · pp. 06–07
Abstract
Let G be a finite group and let G* be the set of elements of prime power order of G. In this paper we show that, if no conjugacy class size of G* is divisible by the product pq, then G is p-nilpotent with abelian Sylow p-subgroup or G is q-nilpotent with abelian Sylow q-subgroup, where p, q are distinct primes.
Finite Group Theory ResearchCoding theory and cryptographySylow theoremsMathematicsConjugacy classAbelian groupNilpotentCombinatoricsExtension (predicate logic)Order (exchange)p-groupPrime (order theory)
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