2019
Том 71
№ 4

# Tyutyanov V. N.

Articles: 3
Brief Communications (Russian)

### Factorizations of Finite Groups into $r$-Soluble Subgroups with Given Embeddings

Ukr. Mat. Zh. - 2014. - 66, № 10. - pp. 1431–1435

Let $X$ be a subset of the set of positive integers. A subgroup $H$ of a group $G$ is called $X$-subnormal in $G$ if there exists a chain of subgroups $H = H_0 ⊆ H_1 ⊆ … ⊆ H_n = G$ such that $|H_i : H_{i-1}| ∈ X$ for all $i$. We study the solubility and $r$ -solubility of a finite group $G = AB$ with some restrictions imposed on the subgroups $A$ and $B$ and on the set $X$ .

Article (Russian)

### On a Hall Hypothesis

Ukr. Mat. Zh. - 2002. - 54, № 7. - pp. 981-990

We obtain a new criterion for the solvability of a finite group with a given family of Hall subgroups.

Brief Communications (Russian)

### On Theorems of the Sylow Type for Finite Groups

Ukr. Mat. Zh. - 2000. - 52, № 10. - pp. 1426-1430

We describe a new class of finite groups for which the D π-theorem is true.