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ON THE NUMBER OF PRIME ORDER SUBGROUPS OF FINITE GROUPS

Part of: Generalizations Representation theory of groups

Published online by Cambridge University Press:  15 December 2009

TIMOTHY C. BURNESS  and
STUART D. SCOTT
TIMOTHY C. BURNESS*
Affiliation:
School of Mathematics, University of Southampton, Southampton SO17 1BJ, UK (email: t.burness@soton.ac.uk)
STUART D. SCOTT
Affiliation:
Department of Mathematics, University of Auckland, Auckland, New Zealand (email: s.scott@auckland.ac.nz)
*
✉For correspondence; e-mail: t.burness@soton.ac.uk
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Abstract

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Let G be a finite group and let δ(G) be the number of prime order subgroups of G. We determine the groups G with the property δ(G)≥∣G∣/2−1, extending earlier work of C. T. C. Wall, and we use our classification to obtain new results on the generation of near-rings by units of prime order.

Keywords

finite groupsprime order subgroupsnear-rings

MSC classification

Secondary: 20D06: Simple groups 16Y30: Near-rings
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 87 , Issue 3 , December 2009 , pp. 329 - 357
Copyright
Copyright © Australian Mathematical Publishing Association, Inc. 2009

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