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# On generalized third dimension subgroups

Published:1998-03-01
Printed: Mar 1998
• Ken-Ichi Tahara
• L. R. Vermani
• Atul Razdan
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## Abstract

Let $G$ be any group, and $H$ be a normal subgroup of $G$. Then M.~Hartl identified the subgroup $G \cap(1+\triangle^3(G)+\triangle(G)\triangle(H))$ of $G$. In this note we give an independent proof of the result of Hartl, and we identify two subgroups $G\cap(1+\triangle(H)\triangle(G)\triangle(H)+\triangle([H,G])\triangle(H))$, $G\cap(1+\triangle^2(G)\triangle(H)+\triangle(K)\triangle(H))$ of $G$ for some subgroup $K$ of $G$ containing $[H,G]$.
 MSC Classifications: 20C07 - Group rings of infinite groups and their modules [See also 16S34] 16S34 - Group rings [See also 20C05, 20C07], Laurent polynomial rings