Title : ( Non-abelian tensor absolute centre of a group )
Authors: Mohammad Reza Hassanlee , Mohammad Reza Rajabzadeh Moghaddam , Mohammad Amin Rostamyari ,
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Abstract
Abstract. In 1904, Schur proved his famous result which says that if the central factor group of a given group is finite then so is its derived subgroup. In 1994, Hegarty showed that if the absolute central factor group, G/L-G-, is finite then so is its autocommutator subgroup, K-G-. Using the notion of non-abelian tensor product, we introduce the concept of tensor absolute centre, $L^\\\\otimes -G-$, and $K^\\\\otimes-G-=G\\\\otimes {\\\\rm Aut}-G-$. Then under some condition we prove that the finiteness of $G/L^\\\\otimes-G-$ implies that $K^\\\\otimes-G-$ is also finite.
Keywords
, Non, abelian tensor product; auto, Engel element; autocommutator subgroup; absolute centre.
@article{paperid:1074216,
author = {محمدرضا حسن لی and Rajabzadeh Moghaddam, Mohammad Reza and محمد امین رستم یاری},
title = {Non-abelian tensor absolute centre of a group},
journal = {Journal of Mathematical Extension},
year = {2019},
volume = {13},
number = {3},
month = {September},
issn = {1735-8299},
pages = {10--18},
numpages = {8},
keywords = {Non-abelian tensor product; auto-Engel element; autocommutator subgroup; absolute centre.},
}
%0 Journal Article
%T Non-abelian tensor absolute centre of a group
%A محمدرضا حسن لی
%A Rajabzadeh Moghaddam, Mohammad Reza
%A محمد امین رستم یاری
%J Journal of Mathematical Extension
%@ 1735-8299
%D 2019
