Zappa, Guido Finite groups in which all non-normal subgroups have the same order. (Italian) Zbl 1097.20020 Atti Accad. Naz. Lincei, Cl. Sci. Fis. Mat. Nat., IX. Ser., Rend. Lincei, Mat. Appl. 13, No. 1, 5-16 (2002). R. Brandl [Commun. Algebra 23, No. 6, 2091-2098 (1995; Zbl 0830.20042)] has asked: given a finite group determine its non-normal subgroups. Let \(G\) be a non-Abelian and non-Hamiltonian finite group and \(n\) an integer \(\geq 2\). A group \(G\) is in the class \(S(n)\) if all its non-normal subgroups have order \(n\). Given a prime number \(p\), the author determines all \(p\)-groups in: (1) \(S(p)\); (2) \(S(p^i)\) with \(i>1\) and \(p\geq 3\). Furthermore, all groups of exponent \(4\) in the class \(S(4)\) are presented. Reviewer: Marek Golasiński (Toruń) Cited in 1 Review MSC: 20D30 Series and lattices of subgroups 20D25 Special subgroups (Frattini, Fitting, etc.) 20D60 Arithmetic and combinatorial problems involving abstract finite groups 20D15 Finite nilpotent groups, \(p\)-groups 20E34 General structure theorems for groups Keywords:finite groups; non-normal subgroups; exponents of groups Citations:Zbl 0830.20042 PDFBibTeX XMLCite \textit{G. Zappa}, Atti Accad. Naz. Lincei, Cl. Sci. Fis. Mat. Nat., IX. Ser., Rend. Lincei, Mat. Appl. 13, No. 1, 5--16 (2002; Zbl 1097.20020)