Subdirect products of finite groups with Hall \(\pi\)-subgroups
Let \(\pi\) be a nonempty set of primes, and let \(E_\pi\) be the class of all finite groups that have Hall \(\pi\)-subgroups. A group that belongs to the class \(E_\pi\) is called an \(E_\pi\)-group. L. A. Shemetkov posed the following question: Is the class \(E_\pi\) closed under finite subdirect products? In the present note we answer this question in the affirmative under the condition that the Schreier conjecture on the solvability of the outer automorphism group of a finite simple group is valid.
scientific article; zbMATH DE number 1028509