• Ram Karan

Articles written in Proceedings – Mathematical Sciences

• Some remarks on subgroups determined by certain ideals in integral group rings

LetG be a group,ZG the integral group ring ofG andI(G) its augmentation ideal. Subgroups determined by certain ideals ofZG contained inI(G) are identified. For example, whenG=HK, whereH, K are normal subgroups ofG andHK⊆ζ(H), then the subgroups ofG determined byI(G)I(H)I(G), andI3(G)I(H) are obtained. The subgroups of any groupG with normal subgroupH determined by (i)I2(G)I(H)+I(G)I(H)I(G)+I(H)I2(G), whenH′⊆[H,G,G] and (ii)I(G)I(H)I(G) when degH2(G/H′, T)≤1, are computed. the subgroup ofG determined byIn(G)+I(G)I(H) whenH is a normal subgroup ofG withG/H free Abelian is also obtained

• Some intersections and identifications in integral group rings

LetZG be the integral group ring of a groupG and I(G) its augmentation ideal. For a free groupF andR a normal subgroup ofF, the intersectionIn+1 (F) ∩In+1 (R) is determined for alln≥ 1. The subgroupsF ∩ (1+ZFI (R) I (F) I (S)) ANDF ∩ (1 + I (R)I3 (F)) of F are identified whenR and S are arbitrary subgroups ofF.

• Some Augmentation Quotients of Integral Group Rings

Let 𝐺 be a group and 𝐻 be a subgroup of 𝐺. A complete description of $\Delta(G)\Delta^n(H)/\Delta^{n+1}(H)$ is given, and as a consequence the structures of $\Delta(G)/\Delta(H)$ and $\Delta^2(G)/\Delta^2(H)$ are determined. Also, the structure of $\Delta^n(G)/\Delta^n(H)$ for all $n\geq 1$ is determined when 𝐺 is a free group.

• # Proceedings – Mathematical Sciences

Current Issue
Volume 129 | Issue 3
June 2019