2017
Том 69
№ 9

Locally soluble AFA-groups

Dashkova O. Yu.

Abstract

Let $A$ be an $\mathbf{R}G$-module, where $\mathbf{R}$ is a ring, $G$ is a locally solvable group, $C_G (A) = 1$, and each proper subgroup $H$ of $G$ for which $A/C_A(H)$ is not an Artinian $\mathbf{R}$-module is finitely generated. It is proved that a locally solvable group $G$ that satisfies these conditions is hyperabelian if R is a Dedekind ring. We describe the structure of $G$ in the case where $G$ is a finitely generated solvable group, $A/C_A(H)$ is not an Artinian $\mathbf{R}$-module and $\mathbf{R}$ is a Dedekind ring.

English version (Springer): Ukrainian Mathematical Journal 65 (2013), no. 4, pp 501-512.

Citation Example: Dashkova O. Yu. Locally soluble AFA-groups // Ukr. Mat. Zh. - 2013. - 65, № 4. - pp. 459-469.

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