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On minimal subgroups of finite groups. (English) Zbl 0930.20021
All groups considered in this paper are finite. Recall that a minimal subgroup of a group is a subgroup of prime order. Recently there has been a considerable interest to study the structure of a group \(G\) under the assumption that all minimal subgroups of \(G\) are well-situated in the group. Ito proved that if the center of a finite group \(G\) of odd order contains all minimal subgroups, then \(G\) is nilpotent. The present paper represents an attempt to extend and improve the results of Ito and some other authors through the theory of formations.

MSC:
20D25 Special subgroups (Frattini, Fitting, etc.)
20D10 Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks
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