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Locally nilpotent groups with weak minimal condition for normal subgroups. (Russian) Zbl 0557.20023
A decreasing chain of subgroups \(G_ 1>G_ 2>..\). is called a decreasing \(\infty\)-chain if every index \(| G_ n:G_{n+1}|\) is infinite. A group G is said to satisfy the weak minimal condition (Min- \(\infty\)-condition) for normal subgroups if every decreasing \(\infty\)- chain of normal subgroups becomes stable. Theorem. Let G be a locally nilpotent group with Min-\(\infty\)-condition for normal subgroups. Then: (1) G satisfies the minimal condition for normal periodic subgroups; (2) G coincides with its hypercentre; (3) G is solvable.
Reviewer: A.G.Gejn

MSC:
20F22 Other classes of groups defined by subgroup chains
20E15 Chains and lattices of subgroups, subnormal subgroups
20F19 Generalizations of solvable and nilpotent groups
20E25 Local properties of groups
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