Let G be a finite group. An element g∈G is a vanishing element of G if there exists an irreducible complex character χ of G such that χ(g) = 0: if this is the case, we say that the conjugacy class of g in G is a vanishing conjugacy class of G. In this paper we show that, if the size of every vanishing conjugacy class of G is not divisible by a given prime number p, then G has a normal p-complement and abelian Sylow p-subgroups.
Groups whose vanishing class sizes are not divisible by a given prime / S. Dolfi, E. Pacifici, L. Sanus. - In: ARCHIV DER MATHEMATIK. - ISSN 0003-889X. - 94:4(2010), pp. 311-317. [10.1007/s00013-010-0107-3]
Groups whose vanishing class sizes are not divisible by a given prime
E. PacificiSecondo
;
2010
Abstract
Let G be a finite group. An element g∈G is a vanishing element of G if there exists an irreducible complex character χ of G such that χ(g) = 0: if this is the case, we say that the conjugacy class of g in G is a vanishing conjugacy class of G. In this paper we show that, if the size of every vanishing conjugacy class of G is not divisible by a given prime number p, then G has a normal p-complement and abelian Sylow p-subgroups.
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10.1007_s00013-010-0107-3.pdf
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