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Some finite solvable groups with non-trivial lattice endomorphisms
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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 ISSN 0004-9727 .
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Official URL: http://dx.doi.org/10.1017/S0004972700037497
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 pā²-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 | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > 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: |
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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 (Creative Commons) |
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