The (2,3)-generation of the finite 8-dimensional orthogonal groups

M. A. Pellegrini; M. C. Tamburini Bellani

The (2,3)-generation of the finite 8-dimensional orthogonal groups

Group Theory 2022-01-04 v1

Authors: M. A. Pellegrini , M. C. Tamburini Bellani

Abstract

We construct $(2,3)$ -generators for the finite $8$ -dimensional orthogonal groups, proving the following results: the groups $\Omega_8^+(q)$ and $P\Omega_8^+(q)$ are $(2,3)$ -generated if and only if $q\geq 4$ ; the groups $\Omega_8^-(q)$ and $P\Omega_8^-(q)$ are $(2,3)$ -generated for all $q\geq 2$ .

Keywords

orthogonal groups (2,3)-generation finite groups generation of groups

Cite

@article{arxiv.2201.00367,
  title  = {The (2,3)-generation of the finite 8-dimensional orthogonal groups},
  author = {M. A. Pellegrini and M. C. Tamburini Bellani},
  journal= {arXiv preprint arXiv:2201.00367},
  year   = {2022}
}

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