Abstract
An element of a group is reversible if it is conjugate to its own inverse, and it is strongly reversible if it is conjugate to its inverse by an involution. A group element is strongly reversible if and only if it can be expressed as a composite of two involutions. In this paper the reversible maps, the strongly reversible maps, and those maps that can be expressed as a composite of involutions are determined in certain groups of piecewise linear homeomorphisms of the real line.
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The authors thank Anthony O’Farrell and the referees for their detailed and helpful remarks. The second author’s work was supported by Science Foundation Ireland grant 05/RFP/MAT0003.
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Gill, N., Short, I. Reversible maps and composites of involutions in groups of piecewise linear homeomorphisms of the real line. Aequat. Math. 79, 23–37 (2010). https://doi.org/10.1007/s00010-010-0002-9
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DOI: https://doi.org/10.1007/s00010-010-0002-9