Stonehewer, Stewart E. and Zacher, G. (2003) Some finite solvable groups with non-trivial lattice endomorphisms. Bulletin of the Australian Mathematical Society , Vol.68 (No.1). pp. 141-153. doi:10.1017/S0004972700037497

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Abstract

The main purpose of this paper is to exhibit a doubly-infinite family of examples which are extensions of a p-group by a p′-group, with the action satisfying some conditions of Zappa (1951), arising from his study of dual-standard (meet-distributive) subgroups. The examples show that Zappa's conditions do not bound the nilpotency class (or even the derived length) of the p-group. The key to this work is found in closely related conditions of Hartley (published here for the first time). The examples use some exceptional relationships between primes.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH):	Lattice theory, Finite groups, Endomorphisms (Group theory), Group theory
Journal or Publication Title:	Bulletin of the Australian Mathematical Society
Publisher:	Cambridge University Press
ISSN:	0004-9727
Official Date:	August 2003
Dates:	Date Event August 2003 Published
Volume:	Vol.68
Number:	No.1
Page Range:	pp. 141-153
DOI:	10.1017/S0004972700037497
Status:	Peer Reviewed
Access rights to Published version:	Open Access

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