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

Mousavi, Hamid

doi:10.22108/ijgt.2023.135678.1814

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	Structure of finite groups with trait of non-normal subgroups II
International Journal of Group Theory
دوره 13، شماره 2، شهریور 2024، صفحه 173-188 اصل مقاله (458.42 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/ijgt.2023.135678.1814
نویسنده
Hamid Mousavi^*
Department of Mathematics, University of Tabriz, P.O.Box 51666-17766, Tabriz, Iran
چکیده
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.
کلیدواژه‌ها
$\NNC$-group؛ $\NAC$-group؛ Non-nilpotent groups

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