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

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