Word maps have large image

Details Word maps have large image Word maps have large image

2002-11-19

arxiv.org/abs/math/0211302v2

Israel J. Math. 139 (2004), 149--156

Mathematics

Group Theory

9 pages; Theorem 1 credited to A. Borel with the relevant bibliographic entry supplied

Scientific paper

An element w in the free group on r letters defines a map f from G^r to G for
each group G. In this note, we show that whenever w is non-trivial and G is a
semisimple algebraic group, f is dominant. When G is a finite simple group, the
ratio \log |f(G^r)| over \log |G| tends to 1 as the order of G tends to
infinity.

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