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

Huang, Feng–Kuo

doi:10.1090/S0002-9939-00-05738-5

Semidirect sum of groups in which endomorphisms are generated by inner automorphisms
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Proc. Amer. Math. Soc. 129 (2001), 629-637 Request permission

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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