Construction of Hurwitz Spaces and Application to the Regular Inverse Problem

Details Construction of Hurwitz Spaces and Application to the Regular Inverse Problem Construction of Hurwitz Spaces and Application to the Regular Inverse Problem

2012-01-06

arxiv.org/abs/1201.1391v2

Mathematics

Number Theory

36 pages

Scientific paper

The author give a simple construction of Hurwitz spaces which is defined by Fried and Volklein, and generalize Hurwitz spaces. As a consequence of this construction, the author prove the regularities of the groups $PSO^+_{n}(\mathbb F_{p^m})$ if $p$ is an odd prime which congruentes with 7 modulo 12, $n$ is an even positive integer grater than 11 and $m=1$ or $p$ is an odd prime which congruentes with 7 modulo 12, $\varphi (p^m-1)/2+1\eqiv n/2 (\mod 2)$, $p^m\equiv 3(\mod 4)$ and $n>\max\{\varphi(p^m-1),7\}$.

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