Narain Gupta's three normal subgroup problem and group homology

Roman Mikhailov,Inder Bir S Passi

doi:10.1016/j.jalgebra.2019.02.007

Narain Gupta's three normal subgroup problem and group homology

Roman Mikhailov, Inder Bir S Passi

Open Access

https://doi.org/10.1016/j.jalgebra.2019.02.007

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Journal: Journal of Algebra	Publication Date: Feb 13, 2019
License type: publisher-specific-oa

Affiliation: Steklov Mathematical Institute, Panjab University, Indian Institute of Science Education and Research Mohali

#Normal Subgroup #Group Ring + Show 8 more

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Abstract

This paper is about application of various homological methods to classical problems in the theory of group rings. It is shown that the third homology of groups plays a key role in Narain Gupta's three normal subgroup problem. For a free group F and its normal subgroups R,S,T, and the corresponding ideals in the integral group ring Z[F], r=(R−1)Z[F],s=(S−1)Z[F],t=(T−1)Z[F], a complete description of the normal subgroup F∩(1+rst) is given, provided R⊆T and the third, fourth and fifth homology groups of R/R∩S are torsion groups.

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