On the norm of the centralizers of a group
Colloquium Mathematicum, Tome 149 (2017) no. 1, pp. 87-91
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
For any group $G$, 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 $n$.
Keywords:
group denote intersection normalizers centralizers elements set define i geq denote infty terminal term ascending series finitely generated group nilpotent only positive integer
Affiliations des auteurs :
Mohammad Zarrin 1
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author = {Mohammad Zarrin},
title = {On the norm of the centralizers of a group},
journal = {Colloquium Mathematicum},
pages = {87--91},
publisher = {mathdoc},
volume = {149},
number = {1},
year = {2017},
doi = {10.4064/cm6965-8-2016},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm6965-8-2016/}
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Mohammad Zarrin. On the norm of the centralizers of a group. Colloquium Mathematicum, Tome 149 (2017) no. 1, pp. 87-91. doi: 10.4064/cm6965-8-2016
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