# Simple groups, permutation groups, and probability

```@article{Liebeck1999SimpleGP,
title={Simple groups, permutation groups, and probability},
author={Martin W. Liebeck and Aner Shalev},
journal={Journal of the American Mathematical Society},
year={1999},
volume={12},
pages={497-520}
}```
• Published 1999
• Mathematics
• Journal of the American Mathematical Society
In recent years probabilistic methods have proved useful in the solution of several problems concerning finite groups, mainly involving simple groups and permutation groups. In some cases the probabilistic nature of the problem is apparent from its very formulation (see [KL], [GKS], [LiSh1]); but in other cases the use of probability, or counting, is not entirely anticipated by the nature of the problem (see [LiSh2], [GSSh]). In this paper we study a variety of problems in finite simple groups…
136 Citations
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In recent yeaxs there has been some research done on the following problem. Given a non-cyclic free group F determine those sets C of groups for which F is residually C . To tackle such a problem it
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