Sadovnichenko O. Investigation of the influence of system of close to normal subgroups on the structure of generalized solvable groups.

The thesis is devoted to studying of infinite dimensional linear groups with some restrictions on system of subspaces. Special approach based on the notion of G-invariance was implemented.Linear groups have played a very important role in algebra. If dimension of vector space A over a field F is finite, n say, then a subgroup G of GL(F,A) can be identified with the group of all invertible n n matrices with entries in F. The subject of finite dimensional linear groups is among the most studied branches of mathematics, having been built using the interplay between algebraic, geometrical, combinatorial and other methods.However, the study of the subgroups of GL(F,A) in the case when A has infinite dimension over F has been much more limited and normally requires some additional restrictions. One natural type of restrictions to use here is a finiteness conditions. The most fruitful example of such restrictions to date has undoubtedly been that of finitary linear groups. A subgroup G of GL(F,A) is called finitary if, for each element g of a group G, the quotient space A/CA(g) has finite dimension over F. The theory of finitary linear groups is now well-established and many interesting results have been proved.