Khazal, R. R. A note on maximal subgroups in finite groups. (English) Zbl 0745.20019 Kyungpook Math. J. 31, No. 1, 83-87 (1991). Here two results are proved. (1) If a finite group \(G\) has exactly two maximal subgroups, then \(G\) is cyclic and \(| G|\) is divisible by two distinct primes. (2) A group \(G\) which has exactly three maximal subgroups and is not a group of prime power order is necessarily cyclic and its order is divisible by at most three primes. Reviewer: Z.Janko (Heidelberg) MSC: 20D15 Finite nilpotent groups, \(p\)-groups 20D25 Special subgroups (Frattini, Fitting, etc.) 20E28 Maximal subgroups 20D30 Series and lattices of subgroups Keywords:\(p\)-groups; finite group; maximal subgroups; cyclic PDF BibTeX XML Cite \textit{R. R. Khazal}, Kyungpook Math. J. 31, No. 1, 83--87 (1991; Zbl 0745.20019)