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S Dolfi, M Herzog, G Kaplan, A Lev

On the size of the nilpotent residual in finite groups

Let G be a finite non-abelian group satisfying Φ(G) = 1 and denote by U the nilpotent residual of G. In this paper, we prove that if G is of odd order then , and if G is of even order not divisible by a Mersenne or a Fermat prime then . These results are best possible and the assumption Φ(G) = 1 cannot be omitted.

Journal of Group Theory, Walter de Gruyter

Print ISSN: 1433-5883
Volume: 10, 05/2007
Pages: 299 - 305

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