Non-nilpotent groups with three conjugacy classes of non-normal subgroups

Document Type : Research Paper

Author

Department of Mathematics, University of Tabriz, P.O.Box 51666-17766, Tabriz, Iran

Abstract

‎For a finite group $G$ let $\nu(G)$ denote the number of conjugacy classes of non-normal subgroups of $G$‎. ‎The aim of this paper is to classify all the non-nilpotent groups with $\nu(G)=3$‎.

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R. Brandl (1995). Groups with few non-normal subgroups. Comm. Algebra. 23 (6), 2091-2098 R. La Haye (1996). Some expicit bounds in groups with a finite number of non-normal subgroups. Comm. Algebra. 25 (12), 3803-3821 H. Mousavi (1999). On finite groups with few non-normal subgroups. Comm. Algebra. 27 (7), 3143-3451 J. J. Rotman (1995). An Introduction to the theory of groups. 4th ed., Springer-Verlag.