Modules over integer group rings of locally soluble groups with minimax restriction
Tóm tắt
Let ℤ be the ring of integers, and A be a ℤG-module, where A/C
A
(G) is not a minimax ℤ-module, C
G
(A) = 1, and G is a locally soluble group. Let L
nm(G) be the system of all subgroups H ≤ G such that quotient modules A/C
A
(H) are not minimax Z-modules. The author studies ℤG-modules A such that L
nm(G) satisfies the minimal condition as an ordered set. It is proved that a locally soluble group G with these conditions is soluble. The structure of the group G is described.
Tài liệu tham khảo
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