Semidirect products of 𝐼-𝐸 groups

Lyons, Carter G.; Peterson, Gary L.

doi:10.1090/S0002-9939-1995-1249885-8

Semidirect products of $I$-$E$ groups
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by Carter G. Lyons and Gary L. Peterson PDF

Proc. Amer. Math. Soc. 123 (1995), 2353-2356 Request permission

Abstract:

An I-E group is a group G in which the endomorphism near-ring generated by the inner automorphisms of G equals the endomorphism near-ring generated by the endomorphisms of G. In this paper we obtain a result characterizing when a semidirect product of I-E groups of relatively prime orders is an I-E group. We then use this result to show that a semidirect product of cyclic groups of relatively prime orders is an I-E group.

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