Semidirect sum of groups in which endomorphisms are generated by inner automorphisms
Author:
FengKuo Huang
Journal:
Proc. Amer. Math. Soc. 129 (2001), 629637
MSC (2000):
Primary 16Y30; Secondary 20E36
Published electronically:
September 20, 2000
MathSciNet review:
1801993
Fulltext PDF Free Access
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Abstract: An IE 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 IE groups to be an IE group is obtained and some wellknown results are generalized. We then use this characterization to prove that a semidirect sum of finite IE groups will again be an IE group if the normal semidirect summand is unique and fully invariant. Conditions for a group to be an IE group are also given.
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Additional Information
FengKuo Huang
Affiliation:
Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana 70504–1010
Email:
fxh2858@usl.edu
DOI:
http://dx.doi.org/10.1090/S0002993900057385
PII:
S 00029939(00)057385
Keywords:
Endomorphism nearring,
IE 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
