Том 70
№ 7

All Issues

Zhang Xirong

Articles: 4
Brief Communications (English)

A note on $SΦ$-supplemented subgroups

Li C., Yi X., Zhang Xirong

↓ Abstract

Ukr. Mat. Zh. - 2016. - 68, № 8. - pp. 1139-1141

We give new and brief proofs of the results obtained by X. Li and T. Zhao in [\mathrm{S}\Phi -supplemented subgroups of finite groups // Ukr. Math. J. – 2012. – 64, № 1. – P. 102–109].

Article (Ukrainian)

Weakly SS-Quasinormal Minimal Subgroups and the Nilpotency of a Finite Group

Zhang Xirong, Zhao Tao

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2014. - 66, № 2. - pp. 187–194

A subgroup H is said to be an s-permutable subgroup of a finite group G provided that the equality HP =PH holds for every Sylow subgroup P of G. Moreover, H is called SS-quasinormal in G if there exists a supplement B of H to G such that H permutes with every Sylow subgroup of B. We show that H is weakly SS-quasinormal in G if there exists a normal subgroup T of G such that HT is s-permutable and H \ T is SS-quasinormal in G. We study the influence of some weakly SS-quasinormal minimal subgroups on the nilpotency of a finite group G. Numerous results known from the literature are unified and generalized.

Brief Communications (English)

On minimal non- MSP -groups

Guo P., Zhang Xirong

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2011. - 63, № 9. - pp. 1279-1278

A finite group $G$ is called an $MSP$-group if all maximal subgroups of the Sylow subgroups of $G$ are Squasinormal in $G$. In this paper, wc give a complete classification of those groups which are not $MSP$-groups but whose proper subgroups are all $MSP$-groups.

Article (English)

Approximation of locally integrable functions on the real line

Stepanets O. I., Wang Kunyang, Zhang Xirong

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1999. - 51, № 11. - pp. 1549–1561

We introduce the notion of generalized \(\bar \psi \) -derivatives for functions locally integrable on the real axis and investigate problems of approximation of the classes of functions determined by these derivatives with the use of entire functions of exponential type.