Structure of finite groups with trait of non-normal subgroups II

Document Type : Research Paper


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


A finite non-Dedekind group $G$ is called an 𝒩𝒜𝒞-group if all non-normal abelian subgroups are cyclic. In this paper, all finite 𝒩𝒜𝒞-groups will be characterized. Also, it will be shown that the center of non-nilpotent 𝒩𝒜𝒞- groups is cyclic. If 𝒩𝒜𝒞-group $G$ has a non-abelian non-normal Sylow subgroup of odd order, then other Sylow subgroups of $G$ are cyclic or of quaternion type.


Main Subjects

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  • Receive Date: 09 November 2022
  • Revise Date: 09 September 2023
  • Accept Date: 09 September 2023
  • Published Online: 01 June 2024