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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
DOI: https://doi.org/10.1090/S0002-9939-00-05738-5
Published electronically: September 20, 2000
MathSciNet review: 1801993
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Abstract:

An I-E group is a group $G$ 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

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