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Orthogonal Isomorphic Representations Of Free Groups

Published online by Cambridge University Press:  20 November 2018

J. De Groot
J. De Groot*
Affiliation:
University of Amsterdam
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1. Introduction. We consider the group of proper orthogonal transformations (rotations) in three-dimensional Euclidean space, represented by real orthogonal matrices (aik) (i, k = 1,2,3) with determinant + 1 . It is known that this rotation group contains free (non-abelian) subgroups; in fact Hausdorff (5) showed how to find two rotations P and Q generating a group with only two non-trivial relations

P2 = Q3 = I.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 8 , 1956 , pp. 256 - 262
Copyright
Copyright © Canadian Mathematical Society 1956

References

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