Abstract
We show that every element of PSL(2, q) is a commutator of elements of coprime orders. This is proved by showing first that in PSL(2, q) any two involutions are conjugate by an element of odd order.
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Bosma W., Cannon J., Playoust C.: The Magma algebra system. I. The user language, J. Symbolic Comput. 24, 235–265 (1997)
L. Dornhoff, Group representation theory. Part A: Ordinary representation theory, Pure and Applied Mathematics, 7. Marcel Dekker, Inc., New York, 1971.
D. Goldstein and R. M. Guralnick, Cosets of Sylow p-subgroups and a Question of Richard Taylor, arXiv:1208.5283.
Gill N., Singh A.: Real and strongly real classes in SL n (q), J. Group Theory 14, 437–459 (2011)
B. Huppert, Endliche Gruppen. I, Die Grundlehren der Mathematischen Wissenschaften, Band 134 Springer-Verlag, Berlin-New York 1967.
Liebeck M.W. et al.: The Ore conjecture, J. Eur. Math. Soc. 12, 939–1008 (2010)
Mihăilescu P.: Primary cyclotomic units and a proof of Catalan’s conjecture, J. Reine Angew. Math. 572, 167–195 (2004)
P. Shumyatsky, Commutators of elements of coprime orders in finite groups, to appear in Forum Mathematicum, arXiv:1208.3177.
Thompson J.G.: On a Question of L. J. Paige, Math. Zeitschr. 99, 26–27 (1967)
Tiep P.H., Zalesski A.E.: Real conjugacy classes in algebraic groups and finite groups of Lie type, J. Group Theory 8, 291–315 (2005)
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The second author was supported by CNPq-Brazil.
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Pellegrini, M.A., Shumyatsky, P. Coprime commutators in PSL(2, q). Arch. Math. 99, 501–507 (2012). https://doi.org/10.1007/s00013-012-0465-0
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DOI: https://doi.org/10.1007/s00013-012-0465-0