2019
Том 71
№ 8

All Issues

Skiba A. N.

Articles: 6
Article (Russian)

On $\Sigma_t^{σ}$ -closed classes of finite groups

Skiba A. N., Zhang Chi

↓ Abstract

Ukr. Mat. Zh. - 2018. - 70, № 12. - pp. 1707-1716

All analyzed groups are finite. Let $\sigma = \{ \sigma_i| i \in I\}$ be a partition of the set of all primes $\mathbb{P}$. If $n$ is an integer, then the symbol $\sigma (n)$ denotes a set $\{\sigma_i| \sigma_i \cap \pi (n) \not = \emptyset\}$. Integers $n$ and $m$ are called $\sigma$ -coprime if $\sigma (n) \cap \sigma (m) = \emptyset$.
Let $t > 1$ be a natural number and let $\mathfrak{F}$ be a class of groups. Then we say that $\mathfrak{F}$ is $\Sigma^{\sigma}_ t$ -closed provided $\mathfrak{F}$ contains each group $G$ with subgroups $A_1, ... ,A_t \in \mathfrak{F}$ whose indices $| G : A_1| ,..., | G : A_t|$ are pairwise $\sigma$ -coprime. We study $\Sigma_t^{σ}$ -closed classes of finite groups.

Article (Russian)

On one generalization of modular subgroups

Skiba A. N., Vasil'ev V. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2011. - 63, № 10. - pp. 1314-1325

We study the influence of generalized modular subgroups on the structure of finite groups.

Article (Russian)

Structure of finite groups with S-quasinormal third maximal subgroups

Lutsenko Yu. V., Skiba A. N.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2009. - 61, № 12. - pp. 1630-1639

We study finite groups whose 3-maximal subgroups are permutable with all Sylow subgroups.

Article (Russian)

$X$-permutable maximal subgroups of Sylow subgroups of finite groups

Guo W., Shum K. P., Skiba A. N.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2006. - 58, № 10. - pp. 1299–1309

We study finite groups whose maximal subgroups of Sylow subgroups are permutable with maximal subgroups.

Article (Russian)

Multiply $\mathfrak{L}$ formations of finite groupsformations of finite groups

Shemetkov L. A., Skiba A. N.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2000. - 52, № 6. - pp. 783-787

We study $\mathfrak{L}$ formations of finite groups.

Article (Ukrainian)

Formations of algebras with complemented subformations

Shemetkov L. A., Skiba A. N.

Full text (.pdf)

Ukr. Mat. Zh. - 1991. - 43, № 7-8. - pp. 1008–1012