In this talk we will discuss :
1. Tensor decompositions of locally matrix algebras and their parametrization by Steinitz numbers.
2. Automorphisms and derivations of locally matrix algebras.
3. Automorphisms and derivations of Mackey algebras and Mackey groups. In particular, we describe automorphisms of all infinite simple finitary torsion groups (in the classification of J.Hall) and derivations of all infinite-dimensional simple finitary Lie algebras (in the classification of A.Baranov and H.Strade).