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A remark on products of locally soluble groups. (English) Zbl 0543.20024
It is shown that if a group G is a product of two normal subgroups, each of which is locally soluble-of-finite-rank, then G is locally soluble if and only if it is locally of finite rank. Thus a group that is locally soluble or locally of finite rank has a unique maximal locally soluble- of-finite-rank normal subgroup.

MSC:
20F19 Generalizations of solvable and nilpotent groups
20E25 Local properties of groups
20E07 Subgroup theorems; subgroup growth
20F16 Solvable groups, supersolvable groups
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References:
[1] Kropholler, Proc. London Math. Soc.
[2] Robinson, Finiteness conditions and generalised soluble groups (1972)
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