2018
Том 70
№ 7

All Issues

Xiaolan Yi

Articles: 2
Article (English)

Finite groups with X-quasipermutable Sylow subgroups

Xiaolan Yi, Xue Yang

↓ Abstract

Ukr. Mat. Zh. - 2015. - 67, № 12. - pp. 1715-1722

Let H ≤ E and X be subgroups of a finite group G. Then we say that H is X-quasipermutable (XS-quasipermutable, respectively) in E provided that G has a subgroup B such that E = NE(H)B and H X-permutes with B and with all subgroups (with all Sylow subgroups, respectively) V of B such that (|H|, |V |) = 1. We analyze the influence of X-quasipermutable and XS-quasipermutable subgroups on the structure of G. In particular, it is proved that if every Sylow subgroup P of G is F(G)-quasipermutable in its normal closure PG in G, then G is supersoluble.

Article (Russian)

Finite Groups with System of SE-Supplemented Subgroups

Shemetkova O. L., Xiaolan Yi

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2013. - 65, № 9. - pp. 1227–1235

We study the influence of the properties of supplemented subgroups on the structure of finite groups. The conditions under which a normal subgroup of a finite group possesses cyclic chief p-factors are obtained.