On the structure of artinian-by-(finite rank) modules over generalized soluble groups

V.A. Chupordia

doi:10.15421/241412

On the structure of artinian-by-(finite rank) modules over generalized soluble groups

V.A. Chupordia (Oles Honchar Dnipropetrovsk National University)

Abstract

Let R be a ring and G a group. An R-module A is said to be artinian-by-(finite rank), if $$$\mathrm{Tor}_R(A)$$$ is artinian and $$$A/\mathrm{Tor}_R(A)$$$ has finite R-rank. In this paper modules A over a group ring $$${\mathbb{Z}}_{p^{\infty}}G$$$ such that $$$A/C_A(H)$$$ is artinian-by-(finite rank) (as an $$${\mathbb{Z}}_{p^{\infty}}$$$-module) for every proper subgroup H are investigated.

Keywords

modules; group rings; modules over group rings; generalized soluble groups; radical groups; artinian modules; generalized radical groups; modules of finite rank

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