Semidirect Products of I - E Groups

Lyons, C. G.; Peterson, Gary L.

doi:10.2307/2161258

Cited by 2 publications

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“…Hence E(S 3 ) illustrates both Corollary 2.3 and 2.4. As a corollary, we obtain one of the main results of C. G. Lyons and G. L. Peterson [10].…”

Section: Corollary 24 Let G Be Semidirect Sum Of a Fully Invariant Subgroup H And A Subgroup K Of G Let P : G → K Be The Projection Map Ssupporting

confidence: 55%

“…J. J. Malone and G. Mason [17] have shown: a semidirect sum of cyclic groups of relatively prime order is I-E when the cyclic normal semidirect summand is the commutator subgroup. C. G. Lyons and G. L. Peterson [10] then made the following improvement: a semidirect sum of cyclic groups of relatively prime order is I-E. Observing that a finite abelian group is I-E if and only if it is cyclic, S. A.…”

Section: Feng-kuo Huangmentioning

confidence: 99%

“…Making use of Proposition 3.1, we can reprove the following corollary by C. G. Lyons and G. L. Peterson [10] without using Corollary 2.5.…”

Section: Direct Sums Of I-e Groupsmentioning

confidence: 99%

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2001

Proc. Amer. Math. Soc.

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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.

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“…Hence E(S 3 ) illustrates both Corollary 2.3 and 2.4. As a corollary, we obtain one of the main results of C. G. Lyons and G. L. Peterson [10].…”

Section: Corollary 24 Let G Be Semidirect Sum Of a Fully Invariant Subgroup H And A Subgroup K Of G Let P : G → K Be The Projection Map Ssupporting

confidence: 55%

Section: Feng-kuo Huangmentioning

confidence: 99%