English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

This paper is about application of various homological methods to classicalproblems in the theory of group rings. It is shown that the third homology ofgroups plays a key role in Narain Gupta's three normal subgroup problem. For afree group $F$ and its normal subgroups $R,\,S,\,T,$ and the correspondingideals in the integral group ring $\mathbb Z[F]$, ${\bf r}=(R-1)\mathbb Z[F],\{\bf s}=(S-1)\mathbb Z[F],\ {\bf t}=(T-1)\mathbb Z[F],$ a complete descriptionof the normal subgroup $F\cap (1+{\bf rst})$ is given, provided $R\subseteq T$and the third and the fourth homology groups of $R/R\cap S$ are torsion groups.

Narain Gupta's three normal subgroup problem and group homology