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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 | ||
[1] A. H. Baartmans and J. J. Woeppel, The automorphism group of a p-group of maximal class with an abelian maximal subgroup, Fund. Math., 93 no. 1 (1976) 41–46. http://matwbn.icm.edu.pl/ksiazki/fm/fm93/fm9316.pdf. [8] The GAP Group, GAP – Groups, Algorithms, and Programming, Version 4.11.0; (2020). https://www.gapsystem.org.
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