On π-Solvable and Locally π-Solvable Groups with Factorization

• Datum: 2001
• Hauptverfasser: Putilov, S. V., Chernikov, N. S., Путилов, С. В., Черников, Н. С.
• Format: Artikel
• Sprache: Russisch; Englisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2001
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/4304
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

We prove that, in a locally π-solvable group G = AB with locally normal subgroups A and B, there exist pairwise-permutable Sylow π′- and p-subgroups A π′, A p and B π′, B p , p ∈ π, of the subgroups A and B, respectively, such that A π′ B π′ is a Sylow π′-subgroup of the group G and, for an arbit...