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Some finite solvable groups with non-trivial lattice endomorphisms

Published online by Cambridge University Press:  17 April 2009

S. E. Stonehewer  and
G. Zacher
S. E. Stonehewer
Affiliation:
Mathematics Institute, University of Warwick, Coventry CV4 7AL, England, Stewart@stonehewer.freeserve.co.uk
G. Zacher
Affiliation:
Dipartimento di Matematica Pura ed Applicata, Università di Padova, Via Belzoni 7, 35131 Padova, Italy, zacher@math.unipd.it
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Abstract

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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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 68 , Issue 1 , August 2003 , pp. 141 - 153
Copyright
Copyright © Australian Mathematical Society 2003

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