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Free k-tuples in linear groups

Published online by Cambridge University Press:  17 April 2009

Arnaldo Mandel  and
Jairo Z. Gonçalves
Arnaldo Mandel
Affiliation:
IMEUSPCx. Postal 20.570, 01000 – São Paulo – SP, Brazil.
Jairo Z. Gonçalves
Affiliation:
IMEUSPCx. Postal 20.570, 01000 – São Paulo – SP, Brazil.
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Abstract

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Let PGL(P) be the group of projective linear transformations of the n-dimensional projective space P over a field F. A topology is given on F, and it is assumed that F is locally-compact; PGL(P) is endowed with the quotient topology from the canonical projection map GL(n, F) → PGL(P), where

.

For any given k, it is shown that the set of k–tuples (g1, g2, … gk) ɛ PGL(P)k which freely generate a free sub-group of PGL(P) and has a nonvoid interior.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 28 , Issue 1 , August 1983 , pp. 151 - 157
Copyright
Copyright © Australian Mathematical Society 1983

References

[1]Chang, Bomshik, Jennings, S.A. and Ree, Rimhak, “On certain pairs of matrices which generate free groups”, Canad. J. Math. 10 (1958), 279–284.CrossRefGoogle Scholar
[2]Dugundji, James, Topology (Allyn and Bacon, Boston, 1966).Google Scholar
[3]Epstein, D.B.A., “Almost all subgroups of a Lie group are free”, J. Algebra 19 (1971), 261–262.CrossRefGoogle Scholar
[4]Lyndon, R.C. and Ullman, J.L., “Pairs of real 2–by–2 matrices that generate free products”, Michigan Math. J 15 (1968), 161–166.CrossRefGoogle Scholar
[5]Macbeath, A.M., “Packings, free products and residually finite groups”, Proc. Cambridge Philos. Soc. 59 (1963), 555–558.CrossRefGoogle Scholar
[6]Mandel, Arnaldo and Gongalves, Jairo Z., “Construction of open sets of free K-tuples of matrices”, submitted.Google Scholar
[7]Tits, J., “Free subgroups in linear groups”, J. Algebra 20 (1972), 250–270.CrossRefGoogle Scholar