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

  • S. V. Putilov
  • N. S. Chernikov

Abstract

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, $$\left( {\prod\nolimits_{p \in {\sigma }} {A_p } } \right)\left( {\prod\nolimits_{p \in {\sigma }} {B_p } } \right)\quad {and}\quad \left( {A_{{\pi }\prime } \prod\nolimits_{p \in {\sigma }} {A_p } } \right)\left( {B_{{\pi }\prime } \prod\nolimits_{p \in {\sigma }} {B_p } } \right)$$ are Sylow σ- and π′ ∪ σ-subgroups, respectively, of the group G.
Published
25.06.2001
How to Cite
PutilovS. V., and ChernikovN. S. “On π-Solvable and Locally π-Solvable Groups With Factorization”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 53, no. 6, June 2001, pp. 840-6, https://umj.imath.kiev.ua/index.php/umj/article/view/4304.
Section
Research articles