پیوندهای مفید
اخبار و اعلانات
آمار
| تعداد نشریات | 44 |
| تعداد شمارهها | 1,851 |
| تعداد مقالات | 14,980 |
| تعداد مشاهده مقاله | 41,752,065 |
| تعداد دریافت فایل اصل مقاله | 16,335,842 |
Finite BCI-groups are solvable | ||
| International Journal of Group Theory | ||
| مقاله 1، دوره 5، شماره 2، شهریور 2016، صفحه 1-6 اصل مقاله (184.55 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2016.7265 | ||
| نویسندگان | ||
| Majid Arezoomand؛ Bijan Taeri* | ||
| Isfahan University of Technology | ||
| چکیده | ||
| Let $S$ be a subset of a finite group $G$. The bi-Cayley graph $BCay(G,S)$ of $G$ with respect to $S$ is an undirected graph with vertex set $G\times\{1,2\}$ and edge set $\{\{(x,1),(sx,2)\}\mid x\in G, \ s\in S\}$. A bi-Cayley graph $BCay(G,S)$ is called a BCI-graph if for any bi-Cayley graph $BCay(G,T)$, whenever $BCay(G,S)\cong BCay(G,T)$ we have $T=gS^\alpha$ for some $g\in G$ and $\alpha\in Aut(G)$. A group $G$ is called a BCI-group if every bi-Cayley graph of $G$ is a BCI-graph. In this paper, we prove that every BCI-group is solvable. | ||
| کلیدواژهها | ||
| Bi-Cayley graph؛ graph isomorphism؛ solvable group | ||
| مراجع | ||
|
M. Arezoomand and B. Taeri (2015) Isomorphisms of finite semi-Cayley graphs Acta Math. Sin. (Engl. Ser.) 31, 715-730
M. Conder and C. H. Li (1998) On isomorphisms of finite Cayley graphs European J. Combin. 19, 911-919
J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson (1985) ATLAS of Finite Groups Oxford Univ. Press, New York
J. D. Dixon and B. Mortimer (1996) Permutation groups New York, Springer-Verlag
E. Dobson and J. Morris (2015) Quotients of CI-groups are CI-groups Graphs Combin. 31, 547-550
F. Harary (1969) Graph theory Addison-Welsey Publishing Company, Reading, Mass.-Menlo Park, Calif.-London
W. Jin and W. Liu (2010) A classification of nonabelian simple 3-BCI-groups European J. Combin. 31, 1257-1264
W. Jin and W. Liu (2011) On Sylow subgroups of BCI groups Util. Math. 86, 313-320
H. Koike and I. Kov\'acs (2014) Isomorphic tetravalent cyclic Haar graphs Ars Math. Contemp. 7, 215-235
H. Koike and I. Kov\'acs (2013) A classification of nilpotent 3-BCI-groups preprint arXiv: 1308.6812v1 [math.GR]
C. H. Li and C. E. Praeger (1997) Finite groups in which any two elements of the same order are either fused or inverse-fused. Comm. Algebra 25, 3081-3118
C. H. Li (1999) Finite CI-groups are soluble Bull. London Math. Soc. 31, 419-423
C. H. Li (2002) On isomorphisms of finite Cayley graphs-a survay Discrete Math. 256, 301-334
S. J. Xu, W. Jin, Q. Shi, Y. Zhu and J. J. Li (2008) The BCI-property of the Bi-Cayley graphs J. Guangxi Norm. Univ.: Nat. Sci. Edition 26, 33-36
| ||
|
آمار تعداد مشاهده مقاله: 3,816 تعداد دریافت فایل اصل مقاله: 3,052 |
||