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Let F be a field and A a vector space over F. Denote by GL(F, A) the group of all F – automorphisms of A. The subgroups of GL(F, A) are called the linear groups. Linear groups play a very important role in algebra and other branches of mathematics. If dim F (A) (the dimension of A over F) is finite, say n, then a subgroup G of GL(F, A) is a finite… (More)

Let G be a group with the property that there are no infinite descending chains of non-subnormal subgroups of G for which all successive indices are infinite. The main result is that if G is a locally (soluble-by-finite) group with this property then either G has all subgroups subnormal or G is a soluble-by-finite minimax group. This result fills a gap left… (More)

A group G has subnormal deviation at most 1 if, for every descending chain H 0 > H 1 >. .. of non-subnormal subgroups of G, for all but finitely many i there is no infinite descending chain of non-subnormal subgroups of G that contain H i+1 and are contained in H i. This property P, say, was investigated in a previous paper by the authors, where soluble… (More)

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