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Presentation of certain Fischer pairs of classical type. (Présentation de certains couples fischériens de type classique.) (French) Zbl 0784.20016
Let \(G\) be a group generated by a class \(D\) of 3-transpositions. The author gives presentations of \(G\) of the form \((X,R)\) with \(X\subseteq D\) in the following cases: (1) \(G\simeq SU(n,2^ 2)\), \(D\) the set of unitary transvections. (2) \(G\) a subgroup of index 2 in \(O(n,3)\), \(D\) a class of reflections \(t_ v\) for \(q(v)\) fixed. Thus \(G\) is obtained as a quotient of a Coxeter group (with suitable diagram) by adding extra relations. For the statements of the main results and the long proofs the reader must be referred to the paper itself. The author obtained [in Geom. Dedicata 41, 275-335 (1992; Zbl 0757.20004)] similar results for the groups \(Sp(2n,2)\).

MSC:
20F05 Generators, relations, and presentations of groups
20F55 Reflection and Coxeter groups (group-theoretic aspects)
20G40 Linear algebraic groups over finite fields
20D06 Simple groups: alternating groups and groups of Lie type
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References:
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