On the linearity of the holomorph group of a free group on two generators
Abstract
Let Fn denote the free group generated by n letters. The purpose of this article is to show that Hol(F2), the holomorph of the free group on two generators, is linear. Consequently, any split group extension of F2 by a linear group H is linear. This result gives a large linear subgroup of Aut(F3). A second application is that the mapping class group for genus one surfaces with two punctures is linear.
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