Abstract
Let F be a field and V a vector space over F. If G is a subgroup of GL(V, F), then we define the central dimension of G (denoted by centdim F G) as the F-dimension of the factor-space V/C V (G). In this paper, we continue the study of locally nilpotent linear groups satisfying the weak minimal or the weak maximal condition on their subgroups of infinite central dimension started in Kurdachenko et al. (Publ Mat 52:151–169, 2008).
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Supported by Proyecto MTM2007-60994 of Dirección General de Investigación MEC (Spain).
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Kurdachenko, L.A., Muñoz-Escolano, J.M., Otal, J. et al. Locally nilpotent linear groups with restrictions on their subgroups of infinite central dimension. Geom Dedicata 138, 69–81 (2009). https://doi.org/10.1007/s10711-008-9299-0
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DOI: https://doi.org/10.1007/s10711-008-9299-0
Keywords
- Infinite dimensional linear group
- Locally nilpotent group
- Weak maximal condition
- Weak minimal condition