Abstract
Let G be a group and H be a subgroup of G. A complete description of Δ(G)Δn(H)/Δn + 1(H) is given, and as a consequence the structures of Δ(G)/Δ(H) and Δ2(G)/Δ2(H) are determined. Also, the structure of Δn(G)/Δn(H) for all n ≥ 1 is determined when G is a free group.
Similar content being viewed by others
References
Gruenberg KW, Cohomological Topics in Group Theory, Lecture Notes in Mathematics, (Berlin: Springer) (1970) vol. 143
Gupta C K, Subgroups induced by certain ideals of free group rings, Comm. Algebra 11 (1983) 2519–2525
Gupta N D, Free Group Rings, Contemporary Math., Amer. Math. Soc. 66 (1987)
Hales A W and Passi I B S, The second augmentation quotient of an integral group ring, Arch. Math. 31 (1978) 259–265
Hurley T and Sehgal S, Groups related to fox subgroups, Comm. Algebra 28 (2000) 1051–1059
Karan Ram and Kumar Deepak, Augmentation quotients of free group rings, Algebra Colloq. 12 (2005) 597–606
Karan Ram and Vermani L R, A note on augmentation quotients, Bull. London Math. Soc. 18 (1986) 5–6
Karan Ram and Vermani L R, Augmentation quotients of integral group rings, J. Indian Math. Soc. 54 (1989) 107–120
Karan Ram and Vermani L R, Augmentation quotients of integral group rings II, J. Pure Appl. Algebra 65 (1990) 253–262
Khambadkone M, Subgroups ideals in group rings I, J. Pure Appl. Algebra 30 (1983) 261–275
Khambadkone M, On the structure of augmentation ideals in group rings, J. Pure Appl. Algebra 35 (1985) 35–45
Khambadkone M, Subgroups ideals in group rings III, Comm. Algebra 14 (1986) 411–421
Losey G, On the structure of Q 2(G) for finitely generated groups, Canad. J. Math. 25 (1973) 353–359
Passi I B S, Polynomial functors, Proc. Cambridge Philos. Soc. 66 (1969) 505–512
Passi I B S, Group Rings and their Augmentation Ideals, Lecture Notes in Mathematics, (Berlin: Springer) (1979) vol. 715
Sandling R, The modular group rings of p-groups, Ph.D. Thesis (University of Chicago) (1969)
Sandling R and Tahara K, Augmentation quotients of group rings and symmetric powers, Math. Proc. Cambridge Philos. Soc. 85 (1979) 247–252
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Gumber, D.K., Karan, R. & Pal, I. Some augmentation quotients of integral group rings. Proc Math Sci 118, 537–546 (2008). https://doi.org/10.1007/s12044-008-0041-5
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12044-008-0041-5