-complementary generations of the Harada-Norton group
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Ali Reza Ashrafi (2003)
Acta Mathematica et Informatica Universitatis Ostraviensis
Sayed, Mohamed (2003)
International Journal of Mathematics and Mathematical Sciences
Klaus Funcke (1975)
Mathematische Zeitschrift
Gert Denk, Wolfgang Metzler (1988)
Fundamenta Mathematicae
Ol'shanskij, A.Yu., Sapir, M.V. (2001)
Electronic Research Announcements of the American Mathematical Society [electronic only]
Alexander Yu. Ol’shanskii, Mark V. Sapir (2003)
Publications Mathématiques de l'IHÉS
S. Peter Farbman (1995)
Publicacions Matemàtiques
The question of whether two parabolic elements A, B of SL2(C) are a free basis for the group they generate is considered. Some known results are generalized, using the parameter τ = tr(AB) - 2. If τ = a/b ∈ Q, |τ| < 4, and |a| ≤ 16, then the group is not free. If the subgroup generated by b in Z / aZ has a set of representatives, each of which divides one of b ± 1, then the subgroup of SL2(C) will not be free.
Wise, Daniel T. (2003)
Electronic Research Announcements of the American Mathematical Society [electronic only]
Stephen G. Brick (1988)
Inventiones mathematicae
Lipschutz, Seymour (1989)
Publications de l'Institut Mathématique. Nouvelle Série
W. Burnside (1899)
Mathematische Annalen
Vershik, A.M. (2000)
Zapiski Nauchnykh Seminarov POMI
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