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

Abstract

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 wellknown 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.