The relative second Fox and third dimension subgroup of arbitrary groups

Details The relative second Fox and third dimension subgroup of arbitrary groups The relative second Fox and third dimension subgroup of arbitrary groups

2007-07-02

arxiv.org/abs/0707.0286v1

Indian J. Pure Appl. Math. 39 (5) (2008), 435-451

Mathematics

Group Theory

17 pages

Scientific paper

Let $I_R(G)$ denote the augmentation ideal of the group algebra $R(G)$ of a
group $G$ with coefficients in a commutative ring $R$. We give a complete
description of the third relative dimension subgroup
$G\cap(1+I_R(K)I_R(G)+I^3_R(G))$ and the second relative Fox subgroup
$G\cap(1+I_R(K)I_R(H)+I^2_R(G)I_R(H))$ for any subgroups $K$ and $H$ of $G$.

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