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arXiv · 1507.03726

On the norm of the centralizers of a group

Mohammad Zarrin
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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.

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Mohammad Zarrin. 2015-07-14. On the norm of the centralizers of a group. https://arxiv.org/abs/1507.03726

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