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- Title
On modules over integer-valued group rings of locally soluble groups with rank restrictions imposed on subgroups.
- Authors
Dashkova, O.
- Abstract
We study a $ \mathbb{Z}G $-module A such that $ \mathbb{Z} $ is the ring of integer numbers, the group G has an infinite sectional p-rank (or an infinite 0-rank), C( A) = 1, A is not a minimax $ \mathbb{Z} $-module, and, for any proper subgroup H of infinite sectional p-rank (or infinite 0-rank, respectively), the quotient module A/ C( H) is a minimax $ \mathbb{Z} $-module. It is shown that if the group G is locally soluble, then it is soluble. Some properties of soluble groups of this kind are discussed.
- Subjects
GROUP theory; RINGS of integers; ALGEBRAIC number theory; QUOTIENT rings; MATHEMATICAL analysis; RING theory
- Publication
Ukrainian Mathematical Journal, 2012, Vol 63, Issue 9, p1379
- ISSN
0041-5995
- Publication type
Article
- DOI
10.1007/s11253-012-0585-5