Geodesic
NIELSEN EQUIVALENCE OF GENERATING PAIRS OF SL(2,q)
Glasgow mathematical journal, Tome 55 (2013) no. 3, pp. 481-509

Voir la notice de l'article provenant de la source Cambridge University Press

We present several conjectures which would describe the Nielsen equivalence classes of generating pairs for the groups SL(2,q) and PSL(2,q). The Higman invariant, which is the union of the conjugacy classes of the commutator of a generating pair and its inverse, and the trace of the commutator play key roles. Combining known results with additional work, we clarify the relationships between the conjectures, and obtain various partial results concerning them. Motivated by the work of Macbeath (A. M. Macbeath, Generators of the linear fractional groups, in Number theory (Proc. Sympos. Pure Math., vol. XII, Houston, TX, 1967) (American Mathematical Society, Providence, RI, 1969), 14–32), we use another invariant defined using traces to develop algorithms that enable us to verify the conjectures computationally for all q up to 101, and to prove the conjectures for a highly restricted but possibly infinite set of q.
DOI : 10.1017/S0017089512000675
Mots-clés : Primary 20F99, Secondary 20G40 
MCCULLOUGH, DARRYL; WANDERLEY, MARCUS. NIELSEN EQUIVALENCE OF GENERATING PAIRS OF SL(2,q). Glasgow mathematical journal, Tome 55 (2013) no. 3, pp. 481-509. doi: 10.1017/S0017089512000675
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