Finitary linear representations of infinite symmetric and alternating groups (Q1346917)

A linear transformation of a vector space is called finitary if it acts identically on some subspace of finite codimension. It is clear that the set of all invertible finitary transformations of a vector space \(V\) is a normal subgroup \(\text{FGL}(V)\) of the group of all invertible linear transformations \(\text{GL}(V)\). A homomorphism of a group \(G\) into \(\text{FGL}(V)\) is called a finitary linear transformation of the group \(G\). The present article is devoted to the study of finitary representations of symmetric and alternating groups of finitary permutations on an infinite set.