English

On the norm of the centralizers of a group

Group Theory 2016-10-31 v1

Abstract

For any group G, let C(G) denote the intersection of the normal- izers of centralizers of all elements of G. Set C0 = 1. Define Ci+1(G)=Ci(G) = C(G=Ci(G)) for i ? 0. By C1(G) denote the terminal term of the ascending series. In this paper, we show that a finitely generated group G is nilpotent if and only if G = Cn(G) for some positive integer n.

Keywords

Cite

@article{arxiv.1507.03726,
  title  = {On the norm of the centralizers of a group},
  author = {Mohammad Zarrin},
  journal= {arXiv preprint arXiv:1507.03726},
  year   = {2016}
}

Comments

group theory