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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

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