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کاربرد نوع شرط:
- جایگاه : پژوهشی
- مجله: Transactions on Combinatorics
- نوع مقاله: Journal Article
- کلمات کلیدی: Bi-Cayley graph,Integer eigenvalues,Representations of finite groups
- چکیده:
- چکیده انگلیسی: The bi-Cayley graph of a finite group $G$ with respect to a subset $Ssubseteq G$, which is denoted by $BCay(G,S)$, is the graph with vertex set $Gtimes{1,2}$ and edge set ${{(x,1), (sx,2)}mid xin G, sin S}$. A finite group $G$ is called a textit{bi-Cayley integral group} if for any subset $S$ of $G$, $BCay(G,S)$ is a graph with integer eigenvalues. In this paper we prove that a finite group $G$ is a bi-Cayley integral group if and only if $G$ is isomorphic to one of the groups $Bbb Z_2^k$, for some $k$, $Bbb Z_3$ or $S_3$.
- انتشار مقاله: 23-04-1393
- نویسندگان: Majid Arezoomand,Bijan Taeri
- مشاهده
- جایگاه : پژوهشی
- مجله: International Journal of Group Theory
- نوع مقاله: Journal Article
- کلمات کلیدی: Finite group,alternating group,cyclic group,join graph
- چکیده:
- چکیده انگلیسی: Let $G$ be a finite group which is not cyclic of prime power order. The join graph $Delta(G)$ of $G$ is a graph whose vertex set is the set of all proper subgroups of $G$, which are not contained in the Frattini subgroup $G$ and two distinct vertices $H$ and $K$ are adjacent if and only if $G=langle H, Krangle$. Among other results, we show that if $G$ is a finite cyclic group and $H$ is a finite group such that $Delta(G)congDelta(H)$, then $H$ is cyclic. Also we prove that $Delta(G)congDelta(A_5)$ if and only if $Gcong A_5$.
- انتشار مقاله: 11-03-1399
- نویسندگان: Zahara Bahrami,Bijan Taeri
- مشاهده
- جایگاه : پژوهشی
- مجله: International Journal of Group Theory
- نوع مقاله: Journal Article
- کلمات کلیدی: Finite groups,minimal non-abelian groups,minimal non-nilpotent groups,critical groups
- چکیده:
- چکیده انگلیسی: We characterize finite non-nilpotent groups $G$ with a unique non-nilpotent proper subgroup. We show that $|G|$ has at most three prime divisors. When $G$ is supersolvable we find the presentation of $G$ and when $G$ is non-supersolvable we show that either $G$ is a direct product of an Schmidt group and a cyclic group or a semi direct product of a $p$-group by a cyclic group of prime power order.
- انتشار مقاله: 06-01-1398
- نویسندگان: Bijan Taeri,Fatemeh Tayanloo-Beyg
- مشاهده
- جایگاه : پژوهشی
- مجله: International Journal of Group Theory
- نوع مقاله: Journal Article
- کلمات کلیدی: Bi-Cayley graph,graph isomorphism,solvable group
- چکیده:
- چکیده انگلیسی: 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 $Gtimes{1,2}$ and edge set ${{(x,1),(sx,2)}mid xin G, sin S}$. 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 $gin G$ and $alphain Aut(G)$. 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.
- انتشار مقاله: 22-01-1393
- نویسندگان: Majid Arezoomand,Bijan Taeri
- مشاهده
- جایگاه : پژوهشی
- مجله: International Journal of Group Theory
- نوع مقاله: Journal Article
- کلمات کلیدی: Thompson's problem,set of the numbers of elements of the same order,order of an element
- چکیده:
- چکیده انگلیسی: Let $pi_e(G)$ be the set of element orders of a finite group $G$. Let $nse(G)={m_nmid ninpi_e(G)}$, where $m_n$ be the number of elements of order $n$ in $G$. In this paper, we prove that if $nse(G)=nse(L_2(81))$, then $Gcong L_2(81)$.
- انتشار مقاله: 16-12-1392
- نویسندگان: Leila Mousavi,Bijan Taeri
- مشاهده
- جایگاه : پژوهشی
- مجله: Algebraic Structures and Their Applications
- نوع مقاله: Journal Article
- کلمات کلیدی: Bi-Cayley graph,Integer eigenvalues,Irreducible representation
- چکیده:
- چکیده انگلیسی: A graph is called integral if all eigenvalues of its adjacency matrix are integers. Given a subset $S$ of a finite group $G$, the bi-Cayley graph $BCay(G,S)$ is a graph with vertex set $Gtimes{1,2}$ and edge set ${{(x,1),(sx,2)}mid sin S, xin G}$. In this paper, we classify all finite groups admitting a connected cubic integral bi-Cayley graph.
- انتشار مقاله: 02-01-1397
- نویسندگان: Majid Arezoomand,Bijan Taeri
- مشاهده