Geodesic
On Generalized Third Dimension Subgroups
Canadian mathematical bulletin, Tome 41 (1998) no. 1, pp. 109-117

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DOI

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 $[H,G]$ .
DOI : 10.4153/CMB-1998-017-1
Mots-clés : 20C07, 16S34 
Tahara, Ken-Ichi; Vermani, L.R.; Razdan, Atul. On Generalized Third Dimension Subgroups. Canadian mathematical bulletin, Tome 41 (1998) no. 1, pp. 109-117. doi: 10.4153/CMB-1998-017-1
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     title = {On {Generalized} {Third} {Dimension} {Subgroups}},
     journal = {Canadian mathematical bulletin},
     pages = {109--117},
     year = {1998},
     volume = {41},
     number = {1},
     doi = {10.4153/CMB-1998-017-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1998-017-1/}
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