2017
Том 69
№ 6

All Issues

Linear groups with minimality condition for some infinite-dimensional subgroups

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

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Abstract

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.

English version (Springer): Ukrainian Mathematical Journal 57 (2005), no. 11, pp 1726-1740.

Citation Example: Dixon M. R., Evans M. J., Kurdachenko L. A. Linear groups with minimality condition for some infinite-dimensional subgroups // Ukr. Mat. Zh. - 2005. - 57, № 11. - pp. 1476–1489.

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