These notes concern aspects of various graphs whose vertex set is a group $ G $ and
whose edges reflect group structure in some way (so that they are invariant under the action …

In earlier work it was shown that each nonabelian finite simple group G has a conjugacy
class C such that, whenever 1≠ x∈ G, the probability is greater than 1/10 that G=〈 x, y〉 for …

Let G be a finite insoluble group with soluble radical R (G). In this paper we investigate the
soluble graph of G, which is a natural generalisation of the widely studied commuting graph …

It is well known that every finite simple group has a generating pair. Moreover, Guralnick and
Kantor proved that every finite simple group has the stronger property, known as $\frac {3}{2} …

In this paper we introduce the graph Γ sc (G) associated with a group G, called the solvable
conjugacy class graph (abbreviated as SCC-graph), whose vertices are the nontrivial …

Let σ={σ i: i∈ I} be a partition of the set P of all prime numbers. A subgroup H of a finite
group G is called σ-subnormal in G if there is a chain of subgroups H= H 0⊆ H 1⊆⋯⊆ H n …

We investigate the relationship between various isomorphism invariants for finite groups.
Specifically, we use the Weisfeiler-Leman dimension (WL) to characterize, compare and …

We give a comprehensive survey of the theory of finite dimensional Lie algebras over an
algebraically closed field of prime characteristic and announce that the classification of all …

The solubility graph associated with a finite group Page 1 International Journal of Algebra and
Computation Vol. 30, No. 8 (2020) 1555–1564 c© World Scientific Publishing Company DOI …

We obtain the following characterization of the solvable radical R (G) of any finite group G: R
(G) coincides with the collection of all g∈ G such that for any 3 elements a1, a2, a3∈ G the …