نتایج جستجو برای: pairwise non commuting elements

تعداد نتایج: 1583407  

پایان نامه :وزارت علوم، تحقیقات و فناوری - دانشگاه شهید باهنر کرمان - دانشکده ریاضی و کامپیوتر 1392

چکیده گراف ناجابجایی از گروه ناآبلی gبه صورت زیر معرفی میشود:به طوریکه راس های گراف ناجابجایی g را مجموعه ی g-z(g)در نظر میگیریم ودوراس x و yتوسط یک یال به هم وصل میشوند اگردوراس باهم جابجا نشوند. در این پایان نامه ثابت میکنیم که اگرg یک گروه متناهی با ?(g)??(sn) آنگاهg?snکه snگروه متقارن n، و nیک عدد طبیعی می باشد. کلمات کلیدی: گراف ناجابجایی، گروه متقارن

A. Bahraini E. Vatandoost, F. Ramezani

Let $R$ be a non-commutative ring with unity. The commuting graph of $R$ denoted by $Gamma(R)$, is a graph with vertex set $RZ(R)$ and two vertices $a$ and $b$ are adjacent iff $ab=ba$. In this paper, we consider the commuting graph of non-commutative rings of order pq and $p^2q$ with Z(R) = 0 and non-commutative rings with unity of order $p^3q$. It is proved that $C_R(a)$ is a commutative ring...

2010
A. Abdollahi A. Azad A. Mohammadi Hassanabadi M. Zarrin Jiping Zhang

Let G be a non-abelian group. The non-commuting graph AG of G is defined as the graph whose vertex set is the non-central elements of G and two vertices are joint if and only if they do not commute. In a finite simple graph Γ, the maximum size of complete subgraphs of Γ is called the clique number of Γ and denoted by ω(Γ). In this paper, we characterize all non-solvable groups G with ω(AG) ≤ 57...

2012
Ali Reza Ashrafi A. Iranmanesh

Given a non-abelian finite group G, let π(G) denote the set of prime divisors of the order of G and denote by Z(G) the center of G. The prime graph of G is the graph with vertex set π(G) where two distinct primes p and q are joined by an edge if and only if G contains an element of order pq and the non-commuting graph of G is the graph with the vertex set G−Z(G) where two non-central elements x...

2015
Maxim Nazarov

This is a joint work with Evgeny Sklyanin. Using the Lax operator formalism, we construct a family of pairwise commuting operators such that the Macdonald symmetric functions of infinitely many variables and of two parameters q,t are their eigenfunctions. We express our operators in terms of the Hall-Littlewood symmetric functions of the same variables and of the parameter t corresponding to th...

2009
Hans Havlicek Boris Odehnal Metod Saniga

There exists a large class of groups of operators acting on Hilbert spaces, where commutativity of group elements can be expressed in the geometric language of symplectic polar spaces embedded in the projective spaces PG(n, p), n being odd and p a prime. Here, we present a result about commuting and non-commuting group elements based on the existence of socalled Möbius pairs of n-simplices, i. ...

Journal: :bulletin of the iranian mathematical society 2013
a. erfanian b. tolue

‎suppose $n$ is a fixed positive integer‎. ‎we introduce the relative n-th non-commuting graph $gamma^{n} _{h,g}$‎, ‎associated to the non-abelian subgroup $h$ of group $g$‎. ‎the vertex set is $gsetminus c^n_{h,g}$ in which $c^n_{h,g} = {xin g‎ : ‎[x,y^{n}]=1 mbox{~and~} [x^{n},y]=1mbox{~for~all~} yin h}$‎. ‎moreover‎, ‎${x,y}$ is an edge if $x$ or $y$ belong to $h$ and $xy^{n}eq y^{n}x$ or $x...

2017
Mai Gehrke Samuel J. v. Gool

It has long been known in universal algebra that any distributive sublattice of congruences of an algebra which consists entirely of commuting congruences yields a sheaf representation of the algebra. In this paper we provide a generalisation of this fact and prove a converse of the generalisation. To be precise, we exhibit a one-to-one correspondence (up to isomorphism) between soft sheaf repr...

2009
A. ABDOLLAHI

Let G be a non-abelian group. The non-commuting graph AG of G is defined as the graph whose vertex set is the non-central elements of G and two vertices are joint if and only if they do not commute. In a finite simple graph Γ the maximum size of a complete subgraph of Γ is called the clique number of Γ and it is denoted by ω(Γ). In this paper we characterize all non-solvable groups G with ω(AG)...

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