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Free k-tuples in linear groups
Published online by Cambridge University Press: 17 April 2009
Abstract
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
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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.
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- Copyright © Australian Mathematical Society 1983
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