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Zariski density and genericity. (English) Zbl 1207.20045
The paper combines a number of results (some due to the author, some not) to show that Zariski density is, in a strong sense, a generic property of subgroups of $$\text{SL}(n,\mathbb{Z})$$ and $$\text{Sp}(2n,\mathbb{Z})$$. Theorem 4.1, stated as a joint result with Ilya Kapovich, asserts that a generic free group automorphism is hyperbolic.
The author is not careful with some statements. For example, in Remark 2.3, $$\mathbb{Z}_p$$ probably means $$G(\mathbb{Z}_p$$). In Theorem 2.6, $$g_p$$ should not be a scalar matrix.

##### MSC:
 20G35 Linear algebraic groups over adèles and other rings and schemes 22E40 Discrete subgroups of Lie groups 20H05 Unimodular groups, congruence subgroups (group-theoretic aspects) 20E07 Subgroup theorems; subgroup growth
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