A new notion derived from the deep commuting graph

Arvin, Bahram; Edalatzadeh, Behrouz; Salemkar, AliReza

doi:10.22108/ijgt.2025.145983.1971

تعداد نشریات	43
تعداد شماره‌ها	1,829
تعداد مقالات	14,878
تعداد مشاهده مقاله	40,792,405
تعداد دریافت فایل اصل مقاله	15,826,449

	A new notion derived from the deep commuting graph
International Journal of Group Theory
دوره 15، شماره 3، آذر 2026، صفحه 135-144 اصل مقاله (435.69 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/ijgt.2025.145983.1971
نویسندگان
Bahram Arvin¹؛ Behrouz Edalatzadeh^* ¹؛ AliReza Salemkar²
¹Department of Mathematics, Faculty of Science, Razi University, Kermanshah, Iran
²Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran
چکیده
The deep commuting graph of a given group $G$ is a graph whose vertex set is $G$, and two elements of $G$ are adjacent if their inverse images in every central extension of $G$ commute. In this paper, we introduce the concept of deep isoclinism for groups and tie this concept to the deep commuting graphs.
کلیدواژه‌ها
Group؛ Graph؛ Deep commuting graph؛ Deep isoclinism

مراجع
[1] Y. Berkovich and Z. Janko, Groups of prime power order, Vol. 1, Walter de Gruyter GmbH & Co. KG, Berlin, 2008. [2] F. R. Beyl, U. Felgner and P. Schmid, On groups occurring as center factor groups, J. Algebra 61 no. 1 (1979) 161–177. [3] F. R. Beyl and J. Tappe, Group extensions, representations, and the Schur multiplicator, Lecture Notes in Mathematics, 958, Springer, Berlin-New York, 1982. [4] R. Brauer and K. A. Fowler, On groups of even order, Ann. of Math. (2), 62 (1955) 565–583. [5] P. J. Cameron, Graphs defined on groups, Int. J. Group Theory 11 no. 2 (2022) 53–107. [6] P. J. Cameron and B. Kuzma, Between the enhanced power graph and the commuting graph, J. Graph Theory, 102 no. 2 (2023) 295–303. [7] P. Hall, The classification of prime-power groups, J. Reine Angew. Math., 182 (1940) 130–141. [8] U. Jezernik and P. Moravec, Commutativity preserving extensions of groups, Proc. Roy. Soc. Edinburgh Ser. A., 148 no. 3 (2018) 575—592. [9] M. R. Jones and J. Wiegold, Isoclinism and covering groups, Bull. Austral. Math. Soc., 11 (1974) 71–76. [10] G. Karpilovsky, The Schur Multiplier, London Mathematical Society Monographs. New Series, 2, The Clarendon Press, Oxford University Press, New York, 1987. [11] C. Miller, The second homology group of a group; relations among commutators, Proc. Amer. Math. Soc., 3 (1952) 588–595. [12] J. C. M. Pezzott and I. N. Nakaoka, On groups whose commuting graph on a transversal is strongly regular, Discrete Math., 342 no. 12 (2019) Article 111626, 8 pp. [13] E. W. Read, On the centre of a representation group, J. London Math. Soc. (2), 16 no. 1 (1977) 43–50. [14] M. Suzuki, Group Theory I, Translated from the Japanese by the author. Grundlehren der Mathematischen Wissenschaften, 247. Springer-Verlag, Berlin-New York, 1982. [15] C. A. Weibel, An introduction to homological algebra, Cambridge Studies in Advanced Mathematics, 38, Cambridge University Press, Cambridge, 1994. [16] K. Yamazaki, On projective representations and ring extensions of finite groups, J. Fac. Sci. Univ. Tokyo Sect. I, 10 (1964) 147–195.
آمار تعداد مشاهده مقاله: 134 تعداد دریافت فایل اصل مقاله: 155

سامانه مدیریت نشریات علمی. طراحی و پیاده سازی از سیناوب

پیوندهای مفید

اخبار و اعلانات

آمار

A new notion derived from the deep commuting graph