关于几乎可解群

本文推广了关于局部有限群的Asar定理及p.Hall—Kulatilaka,Kargapolov定理.

On Almost Solvable Groups

Group G is called almost solvable, if G has a finite normal series such that each factor group of the series is abelian or finite. We show that(1) If locally almost solvable period group G has a finite Sylow p-subgroup, then all Sylow p-subgroups of G are finite and conjuate.(2) Every infinite locally almost solvable group has an infinite abelian subgroup.(3) Suppose that the Sylow p-subgroups of G are locally finite and every finitely generated subgroup of G possesses the "Sylow finite p- property". That is, each finite p-subgroup is isomorphic to some subgroup of each Sylow p-subgroup. If each countable subgroup of G has only countably many Sylow p-subgroups, then all the Sylow p-subgroups of G are conjugate.