Dominions in varieties generated by simple groups. (Q1771941)

An epimorphism in a given category is a right cancellable morphism. Although all epimorphisms in the category of all groups are surjective, this is not true for some subcategories of groups. For example, P.~M.~Neumann exhibited a nonsurjective epimorphism \(A_4\hookrightarrow A_5\) in \(\text{Var}(A_5)\). In the paper, the author generalizes this example by studying a variety of groups generated by finite nonabelian simple groups. The main objective is to construct families of examples of nonsurjective epimorphisms in several varieties.