<i>p</i>-GROUPS WITH CYCLIC OR GENERALISED QUATERNION HUGHES SUBGROUPS: CLASSIFYING TIDY <i>p</i>-GROUPS-Reference-Cited by-同舟云学术

p-GROUPS WITH CYCLIC OR GENERALISED QUATERNION HUGHES SUBGROUPS: CLASSIFYING TIDY p-GROUPS

Published:2023-04-20 Issue:3 Volume:108 Page:443-448
ISSN:0004-9727
Container-title:Bulletin of the Australian Mathematical Society
language:en
Short-container-title:Bull. Aust. Math. Soc.

Author:

BEIKE NICOLAS F.^ORCID,CARLETON RACHEL^ORCID,COSTANZO DAVID G.^ORCID,HEATH COLIN^ORCID,LEWIS MARK L.^ORCID,LU KAIWEN^ORCID,PEARCE JAMIE D.^ORCID

Abstract

AbstractLet G be a p-group for some prime p. Recall that the Hughes subgroup of G is the subgroup generated by all of the elements of G with order not equal to p. In this paper, we prove that if the Hughes subgroup of G is cyclic, then G has exponent p or is cyclic or is dihedral. We also prove that if the Hughes subgroup of G is generalised quaternion, then G must be generalised quaternion. With these results in hand, we classify the tidy p-groups.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference15 articles.

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