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

Graham J. Ellis

doi:10.1090/S0002-9939-98-04440-2

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

Graham J. Ellis

Mathematics

Max-Planck-Institut Für Mathematik

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

14 Citations (Scopus)

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 pⁿ has order |M(G)| ≤ 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.

Original language	English (Ireland)
Pages (from-to)	2513-2523
Number of pages	10
Journal	Proc. Amer. Math. Soc.
Volume	126
Issue number	9
DOIs	https://doi.org/10.1090/S0002-9939-98-04440-2
Publication status	Published - 1 Jan 1998

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Authors
Ellis, Graham

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10.1090/S0002-9939-98-04440-2

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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 pn has order |M(G)| ≤ pd(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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AB - This paper is based on the seemingly new observation that the Schur multiplier M(G) of a d-generator group of prime-power order pn has order |M(G)| ≤ pd(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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A bound for the derived and Frattini subgroups of a prime-power group

Abstract

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