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Let A a vector space over a eld F and let H be a subgroup of GL(F, A). We dene centdimF H to be dimF (A/CA (H)). We say that H has nite central dimension if centdimF H is nite and we say that H has innite central dimension otherwise. We consider soluble linear groups, in which the (ordered by inclusion) set of all subgroups having innite central dimension satises the maximal condition

Linear groups with the maximal condition on subgroups of infinite central dimension