On π-Solvable and Locally π-Solvable Groups with Factorization - Putilov, S. V.; Chernikov, N. S. (Ukrains’kyi Matematychnyi Zhurnal, 2001)
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 \( \subseteq \) π, $$\left( {\prod olimits_{p \in {σ }} {A_p } } \right)\left( {\prod olimits_{p \in {σ }} {B_p } } \right)\quad {and}\quad \left( {A_{{π }′ } \prod olimits_{p \in {σ }} {A_p } } \right)\left( {B_{{π }′ } \prod olimits_{p \in {σ }} {B_p } } \right)$$ are Sylow σ- and π′ ∪ σ-subgroups, respectively, of the group G.