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On Generalized Third Dimension Subgroups

Published online by Cambridge University Press:  20 November 2018

Ken-Ichi Tahara ,
L.R. Vermani  and
Atul Razdan
Ken-Ichi Tahara
Affiliation:
Department of Mathematical Science Aichi University of Education Kariya-shi Japan 448, e-mail: tahara@auems.aichi-edu.ac.jp
L.R. Vermani
Affiliation:
Department of Mathematics Kurukshetra University Kurukshetra 136 119 (Haryana) India, e-mail: kuru@doe.ernet.in
Atul Razdan
Affiliation:
School of Sciences IGNOU, Maidan Garhi New Dehli 110 068 India, e-mail: ignou@giasdl01.vsnl.net.in
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Abstract

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Let $G$ be any group, and $H$ be a normal subgroup of $G$. Then M. Hartl identified the subgroup $G\,\cap \,(1+\,{{\Delta }^{3}}\,(G)\,+\,\Delta (G)\Delta (H))$ of $G$. In this note we give an independent proof of the result of Hartl, and we identify two subgroups $G\,\cap \,(1\,+\,\Delta (H)\Delta (G)\Delta (H)\,+\,\Delta (\left[ H,\,G \right]\Delta (H)),\,G\,\cap \,(1\,+\,{{\Delta }^{2}}\,(G)\Delta (H)\,+\,\Delta (K)\Delta (H))$ of $G$ for some subgroup $K$ of $G$ containing $[H,G]$.

Keywords

20C0716S34
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 41 , Issue 1 , 01 March 1998 , pp. 109 - 117
Copyright
Copyright © Canadian Mathematical Society 1998

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