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arXiv · 0905.0295

On the linearity of the holomorph group of a free group on two generators

F. R. Cohen·V. Metaftsis·S. Prassidis
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Abstract

Let F_n denote the free group generated by n letters. The purpose of this article is to show that Hol(F_2), the holomorph of the free group on two generators, is linear. Consequently, any split group extension of F_2 by a linear group H is linear. This result gives a large linear subgroup of Aut(F_3). A second application is that the mapping class group for genus one surfaces with two punctures is linear.

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F. R. Cohen, V. Metaftsis, S. Prassidis. 2009-05-03. On the linearity of the holomorph group of a free group on two generators. https://arxiv.org/abs/0905.0295

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