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On certain products of soluble groups. (English) Zbl 0984.20016
The authors consider groups \(G=HK\) which are the product of two soluble subgroups \(H\) and \(K\) and satisfy additional permutability requirements, namely that certain subgroups of \(H\) commute with certain subgroups of \(K\). Under these conditions the structure of the factorized group \(G\) is investigated, and it is shown that certain group theoretical properties (in particular finiteness conditions) are inherited by these products. Also bounds for the derived length of these products are given in some cases.

MSC:
20E15 Chains and lattices of subgroups, subnormal subgroups
20F16 Solvable groups, supersolvable groups
20D40 Products of subgroups of abstract finite groups
20E22 Extensions, wreath products, and other compositions of groups
20F14 Derived series, central series, and generalizations for groups
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