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)In(H) (resp., In(H)I(G)I(H)) for n > 1 equals Dn+2(H), the (n + 2)th dimension subgroup of H.
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Communicated by C.K. Gupta
Supported by the National Board for Higher Mathematics, India.
1991 Mathematics Subject Classification: 20C05, 20C07
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Vermani, L.R. Subgroups Determined by Certain Products of Augmentation Ideals. Algebra Colloq. 7, 1–4 (2000). https://doi.org/10.1007/s10011-000-0001-9
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DOI: https://doi.org/10.1007/s10011-000-0001-9