‎let $g$ be a finite group‎. ‎in [ghasemabadi et al.‎, ‎characterizations of the simple group ${}^2d_n(3)$ by prime graph‎ ‎and spectrum‎, ‎monatsh math.‎, ‎2011] it is‎ ‎proved that if $n$ is odd‎, ‎then ${}^2d _n(3)$ is recognizable by‎ ‎prime graph and also by element orders‎. ‎in this paper we prove‎ ‎that if $n$ is even‎, ‎then $d={}^2d_{n}(3)$ is quasirecognizable by‎ ‎prime graph‎, ‎i.e‎...

A code C in the Hamming metric, that is, is a subset of vertex set VΓ graph Γ=H(m,q), gives rise to natural distance partition {C,C1,…,Cρ}, where ρ covering radius C. Such called completely transitive if automorphism group Aut(C) acts transitively on each sets C, C1, …, Cρ. 2-neighbour-transitive ρ⩾2 and C1 C2. Let be binary (q=2) having full minimum δ⩾5. Then it known induces 2-homogeneous act...

Let $$G$$ be a finite group. Its spectrum $$\omega(G)$$ is the set of all element orders . The prime $$\pi(G)$$ divisors order Gruenberg–Kegel graph (or graph) $$\Gamma(G)$$ simple with vertex in which any two vertices $$p$$ and $$q$$ are adjacent if only $$pq\in\omega(G)$$ structural theorem implies that class groups disconnected graphs widely generalizes Frobenius groups, whose role group the...

let $g$ be a finite group. we construct the prime graph of $ g $,which is denoted by $ gamma(g) $ as follows: the vertex set of thisgraph is the prime divisors of $ |g| $ and two distinct vertices $ p$ and $ q $ are joined by an edge if and only if $ g $ contains anelement of order $ pq $.in this paper, we determine finite groups $ g $ with $ gamma(g) =gamma(l_3(q)) $, $2 leq q < 100 $ and prov...

let $g$ be a finite group‎. ‎we say that $g$ has emph{spread} r if for any set of distinct non-trivial elements of $g$ $x:={x_1,ldots‎, ‎x_r}subset g^{#}$ there exists an element $yin g$ with the property that $langle x_i,yrangle=g$ for every $1leq ileq r$‎. ‎we say $g$ has emph{exact spread} $r$ if $g$ has spread $r$ but not $r+1$‎. ‎the spreads of finite simple groups and their decorations ha...