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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

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
Full Text: EuDML