L.Di Martino, M.C.Tamburini and A.Zalesskii: On Hurwitz Groups of Low Rank

dimartino@vmimat.mat.unimi.it, c.tamburini@dmf.bs.unicatt.it, a.zalesskii@uea.ac.uk

Submission: 1999, Nov. 22

A group G is said to be (2,3,7)-generated, or Hurwitz (when finite), if it can be generated by an element of order 2 and an element of order 3 whose product has order 7. Recent constructive results of A.Lucchini, M.C.Tamburini and J.S.Wilson show that the class of (2,3,7)-generated groups is very wide. In particular it contains most finite simple classical groups of high rank. By contrast, in this paper, we use a formula due to L.Scott to show that the Hurwitz linear groups of low rank are very few.

1991 Mathematics Subject Classification: 20G40, 20F05

Keywords and Phrases: Hurwitz groups, classical groups, representations

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