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Linear groups with minimality condition for some infinite-dimensional subgroups

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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 dimF (H) = dimF (A(ωFH)), where ωFH is the augmentation ideal of the group ring FH. The number aug dimF (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.

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Authors and Affiliations

  1. University of Alabama, Tuscaloosa, USA

    M. R. Dixon & M. J. Evans

  2. Dnepropetrovsk University, Dnepropetrovsk

    L. A. Kurdachenko

Authors
  1. M. R. Dixon
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  2. L. A. Kurdachenko
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  3. M. J. Evans
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 11, pp. 1476–1489, November, 2005.

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Dixon, M.R., Kurdachenko, L.A. & Evans, M.J. Linear groups with minimality condition for some infinite-dimensional subgroups. Ukr Math J 57, 1726–1740 (2005). https://doi.org/10.1007/s11253-006-0026-4

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  • DOI: https://doi.org/10.1007/s11253-006-0026-4

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