On the norm of the centralizers of a group
Tom 149 / 2017
Colloquium Mathematicum 149 (2017), 87-91
MSC: Primary 20E34; Secondary 20F45.
DOI: 10.4064/cm6965-8-2016
Opublikowany online: 21 April 2017
Streszczenie
For any group , let C(G) denote the intersection of the normalizers of centralizers of all elements of G. Set C_0= 1. Define C_{i+1}(G)/C_i(G)=C(G/C_i(G)) for i\geq 0. Denote by C_{\infty }(G) the terminal term of this ascending series. We show that a finitely generated group G is nilpotent if and only if G = C_{n}(G) for some positive integer n.
