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Results in Mathematics

, Volume 36, Issue 1–2, pp 160–183 | Cite as

Split Metacyclic p-Groups That Are A-E Groups

  • Gary L. Peterson
Article
  • 13 Downloads

Abstract

A group G is an A-E group if the endomorphism nearring of G generated by its automorphisms equals the endomorphism nearring generated by its endomorphisms. In this paper we set out to determine those p-groups G that are semidirect products of cyclic groups and are A-E groups. We show that no such groups exist when p = 2. When p is odd, we show that G is an A-E group whenever the nilpotency class of G is less than p. Examples are given to show no conclusion can be drawn when the nilpotency class is greater than or equal to p.

1991 Mathematics Subject Classification

Primary 16Y30; Secondary 20D45 20E36 

Key words and phrases

Nearring endomorphism nearring metacyclic p-group 

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Copyright information

© Birkh/:auser Verlag, Basel 1999

Authors and Affiliations

  1. 1.Department of Mathematics James MadisonUniversity HarrisonburgUSA

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