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Semidirect sum of groups in which endomorphisms are generated by inner automorphisms
Author(s):
Feng-Kuo
Huang
Journal:
Proc. Amer. Math. Soc.
129
(2001),
629-637.
MSC (2000):
Primary 16Y30;
Secondary 20E36
Posted:
September 20, 2000
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Abstract:
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:
10.1090/S0002-9939-00-05738-5
PII:
S 0002-9939(00)05738-5
Keywords:
Endomorphism near-ring,
I--E group
Received by editor(s):
May 7, 1999
Posted:
September 20, 2000
Communicated by:
Stephen D. Smith
Copyright of article:
Copyright
2000,
American Mathematical Society
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