On Relative Central Extensions and Covering Pairs

Azam Pourmirzaei; Mitra Hassanzadeh; Behrooz Mashayekhy

On Relative Central Extensions and Covering Pairs

Group Theory 2016-10-04 v1

Authors: Azam Pourmirzaei , Mitra Hassanzadeh , Behrooz Mashayekhy

Abstract

Let $(G,N)$ be a pair of groups. In this article, first we construct a relative central extension for the pair $(G,N)$ such that special types of covering pair of $(G,N)$ are homomorphic image of it. Second, we show that every perfect pair admits at least one covering pair. Finally, among extending some properties of perfect groups to perfect pairs, we characterize covering pairs of a perfect pair $(G,N)$ under some extra assumptions.

Keywords

extension theorems conjugacy classes in groups wreath product of groups

Cite

@article{arxiv.1603.05683,
  title  = {On Relative Central Extensions and Covering Pairs},
  author = {Azam Pourmirzaei and Mitra Hassanzadeh and Behrooz Mashayekhy},
  journal= {arXiv preprint arXiv:1603.05683},
  year   = {2016}
}

Comments

13 pages, to appear in Journal of Algebraic systems

On Relative Central Extensions and Covering Pairs

Abstract

Keywords

Cite

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