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On complemented subgroups of finite groups. (English) Zbl 1157.20323

Summary: A subgroup \(H\) of a group \(G\) is said to be complemented in \(G\) if there exists a subgroup \(K\) of \(G\) such that \(G=HK\) and \(H\cap K=1\). In this paper we determine the structure of finite groups with some complemented primary subgroups, and obtain some new results about \(p\)-nilpotent groups.

MSC:

20D40 Products of subgroups of abstract finite groups
20D15 Finite nilpotent groups, \(p\)-groups
20D20 Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure
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