Y. V. Lavrenyuk, V. V. Nekrashevych, V. I. Sushchansky, “Diagonal direct limits of finite symmetric and alternating groups”, Algebra Discrete Math., 2010, Volume 10, Issue 1,Pages <nobr>67

This article is cited in 2 papers

RESEARCH ARTICLE

Diagonal direct limits of finite symmetric and alternating groups

Y. V. Lavrenyuk^a, V. V. Nekrashevych^b, V. I. Sushchansky^c

^a Kyiv Taras Shevchenko University Mechanics and Mathematics Faculty, Volodymyrska, 60, Kyiv, Ukraine 01033
^b Department of Mathematics Texas A&M University, College Station, TX 77843-3368
^c Institute of Mathematics Silesian University of Technology ul. Kaszubska 23, 44-100 Gliwice, POLAND

Abstract: 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.

MSC: 20F50, 20E32, 20E08, 37A15

Received: 08.04.2010
Revised: 08.04.2010

Language: English