Some finite solvable groups with non-trivial lattice endomorphisms
Stonehewer, Stewart E. (Stewart Edward), 1935- and Zacher, G. (Giovanni). (2003) Some finite solvable groups with non-trivial lattice endomorphisms. Bulletin of the Australian Mathematical Society , Vol.68 (No.1). pp. 141-153. ISSN 0004-9727
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Official URL: http://dx.doi.org/10.1017/S0004972700037497
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|
|Official Date:||August 2003|
|Page Range:||pp. 141-153|
|Access rights to Published version:||Open Access|
 Ft. Crandall, C. Pomerance, Prime numbers, a computational perspective (Springer-Verlag, Berlin, 2001).
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