Geodesic
Diagonal direct limits of finite symmetric and alternating groups
Algebra and discrete mathematics, Tome 10 (2010) no. 1, pp. 67-87

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Diagonal direct limits of permutation groups are studied using their representations by homeomorphisms of the boundary of rooted trees. We describe a new method of classification of such permutation groups, and use this method to find a complete classification of diagonal direct limits of symmetric and alternating groups up to isomorphisms.
Keywords: locally finite simple groups, diagonal embeddings, direct limits, measure-preserving actions. 
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Y. V. Lavrenyuk; V. V. Nekrashevych; V. I. Sushchansky. Diagonal direct limits of finite symmetric and alternating groups. Algebra and discrete mathematics, Tome 10 (2010) no. 1, pp. 67-87. http://geodesic.mathdoc.fr/item/ADM_2010_10_1_a6/