On the number of prime order subgroups of finite groups

Tim C Burness; Stuart Scott

doi:10.1017/S1446788709000226

On the number of prime order subgroups of finite groups

Tim C Burness, Stuart Scott

Research output: Contribution to journal › Article (Academic Journal) › peer-review

6 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	329-357
Number of pages	29
Journal	Journal of the Australian Mathematical Society
Volume	87
DOIs	https://doi.org/10.1017/S1446788709000226
Publication status	Published - 2009

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title = "On the number of prime order subgroups of finite groups",

abstract = "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.",

author = "Burness, \{Tim C\} and Stuart Scott",

year = "2009",

doi = "10.1017/S1446788709000226",

language = "English",

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pages = "329--357",

journal = "Journal of the Australian Mathematical Society",

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T1 - On the number of prime order subgroups of finite groups

AU - Burness, Tim C

AU - Scott, Stuart

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

U2 - 10.1017/S1446788709000226

DO - 10.1017/S1446788709000226

M3 - Article (Academic Journal)

SN - 1446-7887

VL - 87

SP - 329

EP - 357

JO - Journal of the Australian Mathematical Society

JF - Journal of the Australian Mathematical Society

ER -

On the number of prime order subgroups of finite groups

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