Groups with a supersoluble triple factorization
This paper studies groups G which have a triple factorization, a situation which often arises in the study of groups which are expressible as a product of two of their subgroups. That is, \(G=AB=AK=BK\), where A and B are subgroups and K is a normal subgroup of G. The main results all concern the situation where K is hypercentral and this is assumed in their statements below: Theorem A. If A and B are supersoluble then G is supersoluble. - Theorem B. (a) If A and B are locally supersoluble and K is minimax, then G is locally supersoluble. (b) If A and B are hypercyclic and K is minimax, then G is hypercyclic. - Theorem C. If G has finite abelian section rank and A and B are locally supersoluble, then G is locally supersoluble and hence hypercyclic. - The authors give examples to show what limits there are on possible generalizations of these results.
scientific article; zbMATH DE number 4053902
scientific article