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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A bound for the derived and Frattini subgroups of a prime-power group
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by Graham Ellis PDF
Proc. Amer. Math. Soc. 126 (1998), 2513-2523 Request permission

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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Additional Information
  • 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
  • Email: graham.ellis@ucg.ie
  • Received by editor(s): January 27, 1997
  • Communicated by: Ronald M. Solomon
  • © Copyright 1998 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 126 (1998), 2513-2523
  • MSC (1991): Primary 20J05
  • DOI: https://doi.org/10.1090/S0002-9939-98-04440-2
  • MathSciNet review: 1459119