Semidirect sum of groups in which endomorphisms are generated by inner automorphisms

Author:
Feng-Kuo Huang

Journal:
Proc. Amer. Math. Soc. **129** (2001), 629-637

MSC (2000):
Primary 16Y30; Secondary 20E36

Published electronically:
September 20, 2000

MathSciNet review:
1801993

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Abstract | References | Similar Articles | Additional Information

An I-E group is a group in which every endomorphism is finitely generated by its inner automorphisms. In this paper a characterization for a semidirect sum of I-E groups to be an I-E group is obtained and some well-known results are generalized. We then use this characterization to prove that a semidirect sum of finite I-E groups will again be an I-E group if the normal semidirect summand is unique and fully invariant. Conditions for a group to be an I-E group are also given.

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Additional Information

**Feng-Kuo Huang**

Affiliation:
Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana 70504–1010

Email:
fxh2858@usl.edu

DOI:
https://doi.org/10.1090/S0002-9939-00-05738-5

Keywords:
Endomorphism near-ring,
I--E group

Received by editor(s):
May 7, 1999

Published electronically:
September 20, 2000

Communicated by:
Stephen D. Smith

Article copyright:
© Copyright 2000
American Mathematical Society