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PRODUCTS OF ROTATIONS BY A GIVEN ANGLE IN THE ORTHOGONAL GROUP
Part of
M. G. MAHMOUDI
Journal:

Bulletin of the Australian Mathematical Society / Volume 97 / Issue 2 / April 2018

Published online by Cambridge University Press:

02 November 2017, pp. 308-312

Print publication:

April 2018
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For every rotation $\unicode[STIX]{x1D70C}$ of the Euclidean space $\mathbb{R}^{n}$ ($n\geq 3$), we find an upper bound for the number $r$ such that $\unicode[STIX]{x1D70C}$ is a product of $r$ rotations by an angle $\unicode[STIX]{x1D6FC}$ ($0<\unicode[STIX]{x1D6FC}\leq \unicode[STIX]{x1D70B}$). We also find an upper bound for the number $r$ such that $\unicode[STIX]{x1D70C}$ can be written as a product of $r$ full rotations by an angle $\unicode[STIX]{x1D6FC}$.