Search results for " hypercentral groups"

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A note on endomorphisms of hypercentral groups

2002

Abstract Let H be a subnormal subgroup of a hypercentral group G. We prove that endomorphisms of G are uniquely determined by their restrictions to H if and only if Hom(G/HG,G)=0, and draw some consequences from this fact.

Discrete mathematicsSubnormal subgroupAutomorphisms and endomorphisms of groupsPure mathematicsAlgebra and Number TheoryEndomorphismIf and only ifGroup (mathematics)Nilpotent and hypercentral groupsMathematicsJournal of Algebra
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On a result of L.-C. Kappe and M. Newell

2009

There is a long line of research investigating upper central series of a group. The interest comes from the information which these series can give on the structure of a group. Baer (1952) extended the usual notion of center of a group, introducing that of p-centre, where p is a prime. Almost 40 years later, Kappe and Newell (1989) were able to embed the p-centre of a metabelian p-group in the p-th term of the upper central series. This was possible because of the growing knowledge on Engel groups of the 60s years. Here we extend the result of Kappe and Newell (1989) to wider classes of groups.

Settore MAT/02 - Algebrap-hypercentral groups hypercentral groups metabelian p-groupsSettore MAT/03 - Geometria
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