the non commuting graph of a non-abelian finite group $g$ is defined as follows: its vertex set is $g-z(g)$ and two distinct vertices $x$ and $y$ are joined by an edge if and only if the commutator of $x$ and $y$ is not the identity. in this paper we prove some new results about this graph. in particular we will give a new proof of theorem 3.24 of [2]. we also prove that if $g_1$, $g_2$, ..., $...

for a nite group g the commutativity degree denote by d(g) and dend: d(g) = jf(x; y)jx; y 2 g; xy = yxgj jgj2 : in [2] authors found commutativity degree for some groups,in this paper we nd commuta- tivity degree for a class of groups that have high nilpontencies.

The cyclic sieving phenomenon is defined for generating functions of a set affording a cyclic group action, generalizing Stembridge’s q 1⁄4 1 phenomenon. The phenomenon is shown to appear in various situations, involving q-binomial coefficients, Pólya–Redfield theory, polygon dissections, noncrossing partitions, finite reflection groups, and some finite field q-analogues. r 2004 Elsevier Inc. A...

We study the periodic cyclic homology groups of the cross-product of a finite type algebra A by a discrete group Γ. In case A is commutative and Γ is finite, our results are complete and given in terms of the singular cohomology of the sets of fixed points. These groups identify our cyclic homology groups with the “orbifold cohomology” of the underlying (algebraic) orbifold. The proof is based ...

In this note, we show that among finite nilpotent groups of a given order or odd order, the cyclic group has minimum number edges in its subgroup graph. We also conjecture holds for arbitrary groups.

For a simple connected graph G of order n, the normalized Laplacian is square matrix defined as [Formula: see text], where text] diagonal whose i-th entry text]. In this paper, we find eigenvalues joined union regular graphs in terms adjacency and quotient associated with G. finite group power which two distinct vertices are by an edge if only one other. As consequence graphs, investigate cyclic

This note records some observations concerning geodesic growth functions. If a nilpotent group is not virtually cyclic then it has exponential geodesic growth with respect to all finite generating sets. On the other hand, if a finitely generated group G has an element whose normal closure is abelian and of finite index, then G has a finite generating set with respect to which the geodesic growt...

This paper is devoted to the study of lattices generated by finite Abelian groups. Special species of such lattices arise in the exploration of elliptic curves over finite fields. In the case where the generating group is cyclic, they are also known as the Barnes lattices. It is shown that for every finite Abelian group with the exception of the cyclic group of order four these lattices have a ...