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Products of Transvections

Published online by Cambridge University Press:  20 November 2018

B. B. Phadke
B. B. Phadke*
Affiliation:
The Flinders University of South Australia, Bedford Park, South Australia
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This paper is concerned with the presentation of certain elements of the group SL(n, K) as products of a minimal number of transvections. To explain the terminology, let V be an n-dimensional left vector space over a (not necessarily commutative) field K. The group of all non-singular linear transformations of V onto V (i.e. the group of all collineations of V) is the group GL(n, K). This group is generated by collineations leaving a hyperplane pointwise fixed. When n = 2 these collineations are called axial collineations and the invariant hyperplane (line) is then called an axis.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 6 , December 1974 , pp. 1412 - 1417
Copyright
Copyright © Canadian Mathematical Society 1974

References

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