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Subgroups Determined by Certain Products of Augmentation Ideals

Subgroups Determined by Certain Products of Augmentation Ideals Let G be a group, ZG the integral group ring of G, and I(G) its augmentation ideal. Let H be a subgroup of G. It is proved that the subgroup of G determined by the product I(H)I(G)I(H) equals γ3(H), i.e., the third term in the lower central series of H. Also, the subgroup determined by I(H)I(G)I n (H) (resp., I n (H)I(G)I(H)) for n > 1 equals D n+2(H), the (n + 2)th dimension subgroup of H. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Algebra Colloquium Springer Journals

Subgroups Determined by Certain Products of Augmentation Ideals

Algebra Colloquium , Volume 7 (1) – Jan 1, 2000

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Publisher
Springer Journals
Copyright
Copyright © 2000 by Springer-Verlag Hong Kong
Subject
Mathematics; Algebra; Algebraic Geometry
ISSN
1005-3867
eISSN
0219-1733
DOI
10.1007/s10011-000-0001-9
Publisher site
See Article on Publisher Site

Abstract

Let G be a group, ZG the integral group ring of G, and I(G) its augmentation ideal. Let H be a subgroup of G. It is proved that the subgroup of G determined by the product I(H)I(G)I(H) equals γ3(H), i.e., the third term in the lower central series of H. Also, the subgroup determined by I(H)I(G)I n (H) (resp., I n (H)I(G)I(H)) for n > 1 equals D n+2(H), the (n + 2)th dimension subgroup of H.

Journal

Algebra ColloquiumSpringer Journals

Published: Jan 1, 2000

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