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

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Abstract

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 andH∩K⊆ζ(H), then the subgroups ofG determined byI(G)I(H)I(G), andI 3(G)I(H) are obtained. The subgroups of any groupG with normal subgroupH determined by (i)I 2(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 degH 2(G/H′, T)≤1, are computed. the subgroup ofG determined byI n(G)+I(G)I(H) whenH is a normal subgroup ofG withG/H free Abelian is also obtained

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Authors and Affiliations

  1. Department of Mathematics, Kurukshetra University, 132 119, Kurukshetra, India

    L R Vermani, Atul Razdan & Ram Karan

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  1. L R Vermani
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  2. Atul Razdan
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  3. Ram Karan
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Vermani, L.R., Razdan, A. & Karan, R. Some remarks on subgroups determined by certain ideals in integral group rings. Proc. Indian Acad. Sci. (Math. Sci.) 103, 249–256 (1993). https://doi.org/10.1007/BF02866989

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  • DOI: https://doi.org/10.1007/BF02866989

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