The non-isolated vertices in the generating graph of a direct powers of simple groups.
Let \(G\) be a finite group. The generating graph \(L(G)\) of \(G\) has its vertices the set of non-identity elements of \(G\) where two vertices are joined if and only if they generate the group \(G\). Many properties of the group \(G\) can equivalently be stated in terms of \(L(G)\). In the paper under review the authors consider a finite non-Abelian simple group \(G\) and let \(G^d\) be the largest 2-generated power of \(G\), and study behavior of \(L(G^d)\) with respect to that of \(L(G)\).
scientific article; zbMATH DE number 6136609