The $(2,3)$-generation of the finite unitary groups

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

The $(2,3)$-generation of the finite unitary groups

Group Theory 2019-04-26 v3

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

Abstract

In this paper we prove that the unitary groups $SU_n(q^2)$ are $(2,3)$ -generated for any prime power $q$ and any integer $n\geq 8$ . By previous results this implies that, if $n\geq 3$ , the groups $SU_n(q^2)$ and $PSU_n(q^2)$ are $(2,3)$ -generated, except when $(n,q)\in\{(3,2),(3,3),(3,5),(4,2), (4,3),(5,2)\}$ .

Keywords

finite unitary groups (2,3)-generation su_n(q^2) psu_n(q^2) group generation

Cite

@article{arxiv.1807.09270,
  title  = {The $(2,3)$-generation of the finite unitary groups},
  author = {M. A. Pellegrini and M. C. Tamburini Bellani},
  journal= {arXiv preprint arXiv:1807.09270},
  year   = {2019}
}

Comments

In this version, we obtained a complete classification of the finite simple unitary groups which are (2,3)-generated; some proofs have been semplified

The $(2,3)$-generation of the finite unitary groups

Abstract

Keywords

Cite

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