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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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