A characterization of the finite cyclic groups. (English) Zbl 0853.20012

Deaconescu, Marian; Khazal, Reyadh R.

An. Univ. Timiş., Ser. Mat.-Inform. 32, No. 1, 37-40 (1994).

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

Keywords:

finite cyclic groups; intersection of maximal subgroups