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Locally (soluble-by-finite) groups of finite rank. (English) Zbl 0854.20037
The authors prove the following result: A locally (soluble-by-finite) group with all locally soluble subgroups of finite rank is (locally soluble)-by-finite and of finite rank. After they have shown that the group is of finite rank the result follows from a theorem of N. S. Chernikov. Important tools are the use of infinite sequences of groups, one a section of the next, and the classification of finite simple groups.

20E25 Local properties of groups
20F19 Generalizations of solvable and nilpotent groups
20F50 Periodic groups; locally finite groups
20D05 Finite simple groups and their classification
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