Том 71
№ 11

All Issues

Piskun M. M.

Articles: 2
Article (Ukrainian)

On some generalizations of nearly normal subgroups

Piskun M. M., Semko N. N.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2009. - 61, № 10. - pp. 1381-1395

A subgroup $H$ of a group $G$ is called almost polycyclically close to a normal group (in $G$) if $H$ contains a subgroup $L$ normal in $H^G$ for which the quotient group $H^G /L$ is almost polycyclic. The group G is called an anti-$PC$-group if each its subgroup, which is not almost polycyclic, is almost polycyclically close to normal. The structure of minimax anti-$PC$-groups is investigated.

Article (Russian)

On the application of some concepts of ring theory to the study of the influence of systems of subgroups of a group

Piskun M. M., Semko N. N.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2008. - 60, № 5. - pp. 657–668

We study the groups, in which the family Lnon-nn(G) of all not nearly normal subgroups has the Krull dimension. A subgroup H of the group G is said to be nearly normal if H has finite index in its normal closure.