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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