Linear groups saturated by subgroups of finite central dimension
DOI:
https://doi.org/10.15407/dopovidi2019.06.003Keywords:
dense family of subgroups, finite central dimension, infinite groups, infinite-dimensional linear group, linear group, locally soluble groupsAbstract
Let F be a field, A be a vector space over F, and G be a subgroup of GL(F, A). We say that G has a dense family of subgroups having finite central dimension, if, for every pair of subgroups H, K of G such that H ≤ K and H is not maximal in K, there exists a subgroup L of finite central dimension such that H ≤ L ≤ K (we can note that L can match with one of the subgroups H or K). We study locally solvable linear groups with a dense family of subgroups having finite central dimension.
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