On π-Solvable and Locally π-Solvable Groups with Factorization
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 arbitrary nonempty set σ \( \) π, ( olimits_p σ A_p )( olimits_p σ B_p )and( A_π ′ olimits_p σ A_p )( B_π ′ olimits_p σ B_p ) are Sylow σ- and π′ ∪ σ-subgroups, respectively, of the group G., number=6, journal=Ukrains’kyi Matematychnyi Zhurnal, author=Putilov, S. V. and Chernikov, N. S., year=2001, month=Jun., pages=840–846