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

Ellis, Graham

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

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

Proc. Amer. Math. Soc. 126 (1998), 2513-2523

DOI: https://doi.org/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 $p^n$ 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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