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- W2740525018 abstract "In cite{jpsf} we constructed pairs of units $u,v$ in $Z$-orders of a quaternion algebra over $Q (sqrt{-d})$, $d equiv 7 pmod 8$ positive and square free, such that is free for some $nin mathbb{N}$. Here we extend this result to any imaginary quadratic extension of $ mathbb{Q}$, thus including matrix algebras. More precisely, we show that is a free group for all $ngeq 1$ and $d>2$ and for $d=2$ and all $ngeq 2$. The units we use arise from Pell's and Gauss' equations. A criterion for a pair of homeomorphisms to generate a free semigroup is also established and used to prove that two certain units generate a free semigroup but that, in this case, the Ping-Pong Lemma can not be applied to show that the group they generate is free." @default.
- W2740525018 created "2017-08-08" @default.
- W2740525018 creator A5048368023 @default.
- W2740525018 date "2009-01-14" @default.
- W2740525018 modified "2023-09-26" @default.
- W2740525018 title "Construting Free Groups in Quaternion Algebras" @default.
- W2740525018 hasPublicationYear "2009" @default.
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