2019
Том 71
№ 1

# On modules over integer-valued group rings of locally soluble groups with rank restrictions imposed on subgroups

Dashkova O. Yu.

Abstract

We study the $ZG$-module $A$ such that $Z$ is the ring of integers, the group $G$ has infinite section $p$-rank (or infinite 0-rank), $C_G(A) = 1$, $A$ is not a minimax $Z$-module, and, for every proper subgroup $H$ of infinite section $p$-rank (or infinite 0-rank, respectively), the quotient module $A/C_A(H)$ is a minimax $Z$-module. It is proved that if the group $G$ under consideration is locally solvable, then $G$ is a solvable group. Some properties of a solvable group of this type are obtained.

English version (Springer): Ukrainian Mathematical Journal 63 (2011), no. 9, pp 1379-1389.

Citation Example: Dashkova O. Yu. On modules over integer-valued group rings of locally soluble groups with rank restrictions imposed on subgroups // Ukr. Mat. Zh. - 2011. - 63, № 9. - pp. 1206-1217.

Full text