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A bound for the derived and Frattini subgroups of a prime-power group

Author: Graham Ellis
Journal: Proc. Amer. Math. Soc. 126 (1998), 2513-2523
MSC (1991): Primary 20J05
MathSciNet review: 1459119
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Abstract: This paper is based on the seemingly new observation that the Schur multiplier $M(G)$ of a $d$-generator group of prime-power order $p^n$ has order $|M(G)|\le p^{d(2n-d-1)/2}$. We prove several related results, including sufficient conditions for a sharper bound on $|M(G)|$ to be an equality.

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Graham Ellis
Affiliation: Department of Mathematics, University College, Galway, Ireland
Address at time of publication: Max-Planck-Institut für Mathematik, Gottfried-Claren-Straße 26, Bonn, Germany

Received by editor(s): January 27, 1997
Communicated by: Ronald M. Solomon
Article copyright: © Copyright 1998 American Mathematical Society