Direct limits of symmetric and alternating groups with strictly diagonal embeddings

Abstract.

In this paper we investigate the locally finite groups which are direct limits of finite symmetric or alternating groups. Our main result is to complete classification of limit groups of direct systems of symmetric or alternating groups with the strictly diagonal embeddings. It is similar to Glim's classification. We construct the transversal consisting of pairwise non-isomorphic groups and prove that these groups, considered as subgroups of the symmetric group $S({\Bbb N})$, form a lattice which is isomorphic to the lattice of supernatural numbers (ordered by the divisibility).