let $g$ be a non-abelian finite group. in this paper, we prove that $gamma(g)$ is $k_4$-free if and only if $g cong a times p$, where $a$ is an abelian group, $p$ is a $2$-group and $g/z(g) cong mathbb{ z}_2 times mathbb{z}_2$. also, we show that $gamma(g)$ is $k_{1,3}$-free if and only if $g cong {mathbb{s}}_3,~d_8$ or $q_8$.

Motivated by quantum simulation, we consider lattice Hamiltonians for Yang-Mills gauge theories with finite group, example a subgroup of compact Lie group. We show that the electric Hamiltonian admits an interpretation as certain natural, nonunique Laplacian operator on Abelian or non-Abelian group and derive some consequences from this fact. Independent chosen Hamiltonian, provide full explici...

We study the base sizes of finite quasiprimitive permutation groups twisted wreath type, which are precisely with a unique minimal normal subgroup that is also non-abelian, non-simple and regular. Every group type isomorphic to product G=Tk:P acting on its Ω=Tk, where T some non-abelian simple P transitively k={1,…,k} k⩾2. prove if G primitive Ω k, then has size 2. proportion pairs points bases...

On the projective plane there is a unique cubic root of canonical bundle and this acyclic. fake planes such exists if are no 3-torsion divisors (and usually exists, but not unique, otherwise). Earlier we conjectured that any must be In present note give two short proofs statement show acyclicity some other line bundles on with at least $9$ automorphisms. Similarly to our earlier work employ sim...

The non-commuting graph $Gamma(G)$ of a non-abelian group $G$ with the center $Z(G)$ is a graph with thevertex set $V(Gamma(G))=Gsetminus Z(G)$ and two distinct vertices $x$ and $y$ are adjacent in $Gamma(G)$if and only if $xy neq yx$. The aim of this paper is to compute the spectra of some well-known NC-graphs.

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...