Near-Rings and Rings Generated by Homomorphisms on Groups

Birkenmeier, Gary F.; Heatherly, Henry E.; Pilz, Günter

doi:10.1007/978-94-009-1481-0_11

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Theorem 61 (Malone) Let G Be a Group With The E → D Proper1

Examples and Constructions1

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Cited by 5 publications

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“…We will let O G denote the zero element of the near-ring (H (G, K) , +, •) and we will assume H is non-trivial and let H # denote the set H {O G }. Note that Birkenmeier, Heatherly and Pilz [1], [2] initiated the study of the H (G, K) substructure.…”

Section: Theorem 61 (Malone) Let G Be a Group With The E → D Propermentioning

confidence: 99%

An interesting orbit-induced partition of the class of all groups

Boudreaux

2007

imf

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Given that the set of endomorphisms of a group is contained in the set of distributive elements of its endomorphism near-ring, which, in turn, is contained in the endomorphism near-ring, we show that the class of all groups is partitioned into four nonempty subclasses when all combinations of these inclusions, proper or non-proper, are considered. Furthermore, a characterization of each subclass is given in terms of the orbits of the underlying group. Mathematics Subject Classification: 20E99

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Section: Theorem 61 (Malone) Let G Be a Group With The E → D Propermentioning

confidence: 99%