Abstract:For a finite group G and an inverse-closed generating set C of G, let Aut(G; C) consist of those automorphisms of G which leave C invariant. We define an Aut(G; C)-invariant normal subgroup Φ(G; C) of G which has the property that, for any Aut(G; C)-invariant normal set of generators for G, if we remove from it all the elements of Φ(G; C), then the remaining set is still an Aut(G; C)invariant normal generating set for G. The subgroup Φ(G; C) contains the Frattini subgroup Φ(G) but the inclusion may be proper. … Show more
Set email alert for when this publication receives citations?
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.