2019
Том 71
№ 8

All Issues

Evans M. J.

Articles: 2
Article (Russian)

Linear groups with minimality condition for some infinite-dimensional subgroups

Dixon M. R., Evans M. J., Kurdachenko L. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2005. - 57, № 11. - pp. 1476–1489

Let $F$ be a field, let $A$ be a vector space over $F$, and let $GL(F, A)$ be the group of all automorphisms of the space $A$. If $H$ is a subgroup of $GL(F, A)$, then we set aug $\dim_F (H) = \dim_F (A(ωFH))$, where $ωFH$ is the augmentation ideal of the group ring $FH$. The number ${\rm{aug} \dim}_F (H)$ is called the augmentation dimension of the subgroup $H$. In the present paper, we study locally solvable linear groups with minimality condition for subgroups of infinite augmentation dimension.

Article (English)

Groups with Various Minimal Conditions on Subgroups

Dixon M. R., Evans M. J., Smith H.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2002. - 54, № 6. - pp. 780-788

We briefly review some recent works on groups with the weak minimal condition on nonnilpotent subgroups. We also study the class of groups with the weak minimal condition on non-(soluble of derived length d) subgroups.