Groups in which prime order elements commute

Das, Angsuman; Mandal, Arnab

doi:10.22108/ijgt.2025.143874.1939

تعداد نشریات	43
تعداد شماره‌ها	1,802
تعداد مقالات	14,715
تعداد مشاهده مقاله	39,774,176
تعداد دریافت فایل اصل مقاله	15,440,721

	Groups in which prime order elements commute
International Journal of Group Theory
دوره 15، شماره 1، خرداد 2026، صفحه 17-26 اصل مقاله (479.77 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/ijgt.2025.143874.1939
نویسندگان
Angsuman Das^* ؛ Arnab Mandal
Department of Mathematics, Presidency University Kolkata, India
چکیده
It is known that if $G$ is a finite group in which all the elements of prime power order commute, then $G$ is abelian. However, the same does not hold if prime power is replaced by prime. In this article, we introduce the study of a class of finite groups $G$ in which the prime order elements commute. In particular, we discuss the relationship between these class of groups with other known classes of finite groups, like simple groups, perfect groups etc. Moreover, we also prove some results on the possible orders of such groups. Finally, we conclude with some open issues and observations supported by computational evidences using GAP.
کلیدواژه‌ها
perfect group؛ commuting elements؛ characteristic subgroup

مراجع
[1] K. Conrad, Supgroup series II, Lecture Notes available at https://kconrad.math.uconn.edu/blurbs/grouptheory/subgpseries2.pdf. [2] The GAP Group, GAP – Groups, Algorithms, and Programming, Version 4.12.2 ; 2022, https://www.gap-system.org. [3] D. Gorenstein, Finite groups, AMS Chelsea Publishing, New York, 1968. [4] D. J. S. Robinson, A course in the theory of groups, 2nd Edition, Graduate Text in Mathematics, Springer, New York, 1996. [5] M. Suzuki, Group theory I, Springer Berlin, Heidelberg, 1982.
آمار تعداد مشاهده مقاله: 152 تعداد دریافت فایل اصل مقاله: 206

سامانه مدیریت نشریات علمی. طراحی و پیاده سازی از سیناوب

پیوندهای مفید

اخبار و اعلانات

آمار

Groups in which prime order elements commute