In this article, using the concept of generalized Baer-invariant of a pair of groups, we establish some related isomorphisms between lower marginal quotient pairs of groups, which are generalized versions of some isomorphisms of Stallings. We also derive a result for the pair to be an ultra Hall pair for special varieties of groups. This result generalizes that of Fung in 1977, which has roots in Philip Hall’s criterion on nilpotency.
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@article{CRMATH_2021__359_5_631_0,
author = {Rismanchian, Mohammad Reza},
title = {Group extensions and marginal series of pair of groups},
journal = {Comptes Rendus. Math\'ematique},
pages = {631--638},
publisher = {Acad\'emie des sciences, Paris},
volume = {359},
number = {5},
year = {2021},
doi = {10.5802/crmath.212},
language = {en},
url = {http://www.numdam.org/articles/10.5802/crmath.212/}
}
TY - JOUR AU - Rismanchian, Mohammad Reza TI - Group extensions and marginal series of pair of groups JO - Comptes Rendus. Mathématique PY - 2021 SP - 631 EP - 638 VL - 359 IS - 5 PB - Académie des sciences, Paris UR - http://www.numdam.org/articles/10.5802/crmath.212/ DO - 10.5802/crmath.212 LA - en ID - CRMATH_2021__359_5_631_0 ER -
%0 Journal Article %A Rismanchian, Mohammad Reza %T Group extensions and marginal series of pair of groups %J Comptes Rendus. Mathématique %D 2021 %P 631-638 %V 359 %N 5 %I Académie des sciences, Paris %U http://www.numdam.org/articles/10.5802/crmath.212/ %R 10.5802/crmath.212 %G en %F CRMATH_2021__359_5_631_0
Rismanchian, Mohammad Reza. Group extensions and marginal series of pair of groups. Comptes Rendus. Mathématique, Tome 359 (2021) no. 5, pp. 631-638. doi : 10.5802/crmath.212. http://www.numdam.org/articles/10.5802/crmath.212/
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