اخبار و اعلانات

 آمار

تعداد نشریات44
تعداد شماره‌ها1,877
تعداد مقالات15,278
تعداد مشاهده مقاله43,731,183
تعداد دریافت فایل اصل مقاله17,563,283
Darafsheh, Mohammad Reza, Yousefzadeh, Pedram. (1392). Characterization of the symmetric group by its non-commuting graph. , 2(2), 47-72. doi: 10.22108/ijgt.2013.1920
Mohammad Reza Darafsheh; Pedram Yousefzadeh. "Characterization of the symmetric group by its non-commuting graph". , 2, 2, 1392, 47-72. doi: 10.22108/ijgt.2013.1920
Darafsheh, Mohammad Reza, Yousefzadeh, Pedram. (1392). 'Characterization of the symmetric group by its non-commuting graph', , 2(2), pp. 47-72. doi: 10.22108/ijgt.2013.1920
Darafsheh, Mohammad Reza, Yousefzadeh, Pedram. Characterization of the symmetric group by its non-commuting graph. , 1392; 2(2): 47-72. doi: 10.22108/ijgt.2013.1920

Characterization of the symmetric group by its non-commuting graph

International Journal of Group Theory
مقاله 7، دوره 2، شماره 2، شهریور 2013، صفحه 47-72    اصل مقاله (323.54 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/ijgt.2013.1920
نویسندگان
Mohammad Reza Darafsheh1؛ Pedram Yousefzadeh* 2
1University of Tehran
2K. N. Toosi University of Technology
چکیده
‎The non-commuting graph $\nabla(G)$ of a non-abelian group $G$ is defined as‎ ‎follows‎: ‎its vertex set is $G-Z(G)$ and two distinct vertices $x$ and $y$ are‎ ‎joined by an edge if and only if the commutator of $x$ and $y$ is not the‎ ‎identity‎. ‎In this paper we prove that if $G$ is a finite group with‎ ‎$\nabla(G) \cong \nabla(BS_n)$‎, ‎then $G \cong BS_n$‎, ‎where $BS_n$‎ ‎is the symmetric group of degree $n$‎, ‎where $n$ is a natural number‎.
کلیدواژه‌ها
Keywords and phrases: non-commuting graph؛ symmetric group؛ Finite groups
مراجع
A. Abdollahi, S. Akbari and H. R. Maimani (2006) Non-commting graph of a group J. Algebra 298, 468-492
E. Artin (1955) The orders of the linear groups Comm. Pure Appl. Math. 8, 355-365
E. Artin (1955) The orders of the classical simple groups Comm. Pure Appl. Math. 8, 455-472
M. R. Darafsheh (2009) Groups with the same non-commutng graph Discrete Appl. Math. 157 (4), 833-837
M. R. Darafsheh and P. Yousefzadeh A characterization of the group $\BA_{22}$ by non-commuting graph to appear in Bull. Korean Math. Soc.
R. Solomon and A. Woldar (2012) All simple groups are charcterized by their non-commuting graphs preprint
S. H. Alavi and A. Daneshkhah (2005) A new characterization of alternating and symmetric groups J. Appl. Math. Comput. 17, 245-258
آمار
تعداد مشاهده مقاله: 5,235
تعداد دریافت فایل اصل مقاله: 3,333


سامانه مدیریت نشریات علمی. طراحی و پیاده سازی از سیناوب