A probabilistic Tits alternative and probabilistic identities
A probabilistic Tits alternative and probabilistic identities
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概率 Tits 替代方案和概率恒等式
DOI：
10.2140/ant.2016.10.1359
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
A. Shalev
中科院分区：
文献类型：
--
作者：
M. Larsen;A. Shalev
We introduce the notion of a probabilistic identity of a residually finite group. We prove that a finitely generated linear group satisfies a probabilistic identity if and only if it is virtually solvable.
As an application, we prove a probabilistic variant of the Tits alternative: let G be the profinite completion of a finitely generated linear group. Then either G is virtually solvable, or for any positive integer n, with probability one, n independent, uniformly distributed elements of G freely generate a free subgroup of G of rank n.
