Let A be an R G-module, where R is a ring, G is a locally soluble group, C G (A) = 1; and every proper subgroup H of G for which A = C A (H) is not an Artinian R-module is finitely generated. It is shown that a locally soluble group G satisfying these conditions is hyper-Abelian if R is a Dedekind ring. We describe the structure of the group G in the case where G is a finitely generated soluble group, A = C A (G) is not an Artinian R-module, and R is a Dedekind ring.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, No. 4, pp. 459–469, April, 2013.
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Dashkova, O.Y. Locally soluble AFA-groups. Ukr Math J 65, 501–512 (2013). https://doi.org/10.1007/s11253-013-0791-9
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DOI: https://doi.org/10.1007/s11253-013-0791-9