In this paper, we investigate the notion of isoclinism on a pair of n-Lie algebras, which forms an equivalence relation. In addition, we prove each equivalence class contains a stem pair of n-Lie algebras, which has minimal dimension among...

In this talk, we discuss this notion in Lie algebras and give some

results similar to N.S. Hekster in 1986. In particular, it is shown that

every family of n-isoclinism of Lie algebras contains an n-stem Lie

algebra of minimal...

Abstract: Let G be a finite group. In this paper we introduce the generalized conjugate graph Γc

(G,n)

which is a graph whose vertices are all the non-central subsets of G with n elements and two distinct

P. Hall introduced the notion of isoclinism in order to classify groups of prime power order.

The notion of isoclinism can be simulated for pairs (G;N) of groups, in which G is a group and N

is a normal subgroup. This talk verifies...

Let G be a group and Zn(G) be the n-th term of upper central series of G, for every n ≥ 1. The n-th central graph of G denoted by Γn z (G) is a simple graph whose vertices are elements of G and two distinct vertices x and ...

‎The equivalence relation isoclinism partitions the class of all pairs of groups‎

‎into families‎. ‎In this paper‎, ‎a complete classification of the set of all pairs $(G,G')$ is established‎, ‎whenever $G$ is a $p$-group of order at most $p...

Abstract In this paper, we introduce the new concept isoclinism of two non-commuting graphs. We describe it with this hope to determine the properties of the graph with large number of vertices and edges more easier by use of its smaller...

‎In this talk we focus on groups as $G$ such that $G'\\cap \\phi(G)=1.$ It is shown that each $n$-isoclinism family of these groups has a unique $n$-stem group and also every $(n+1)$-isoclinism induces an $n$-isoclinism‎. ‎Moreover‎, ‎some...

In any finite group G, the commutativity degree of G (denoted

by d(G)) is the probability that two randomly chosen elements of G commute.

More generally, for every n ≥ 2 the nth commutativity degree

(denoted ...

In 1940, P. Hall introduced the concept of isoclinism of groups. In the

present paper, we introduce the notion of tensor isoclinism between

two groups. Among other results it is shown that the tensor degree of

a given group G...