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A characterization of the finite cyclic groups. (English) Zbl 0853.20012
Summary: We prove that a finite group \(G\) is cyclic iff \(G=\langle H,\widetilde H_G\rangle\) for every \(H\leq G\), where \(\widetilde H_G\) is the intersection of those maximal subgroups of \(G\) which do not contain \(H\).

MSC:
20D30 Series and lattices of subgroups
20E28 Maximal subgroups
20D25 Special subgroups (Frattini, Fitting, etc.)
20F05 Generators, relations, and presentations of groups
20E34 General structure theorems for groups
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