Computational Methods and Function Theory 8 (2008), No. 1, 173--193
Copyright Heldermann Verlag 2008
Anthony G. O'Farrell
anthonyg.ofarrell@gmail.com , National University of Ireland, Mathematics Department, Co. Kildare, Ireland.
For each natural number $n$, we characterise the invertible series (under composition) that are the composition of $n$ proper involutions. We work with formal power series in one variable over a field of characteristic zero. We also describe the \emph{reversible} series (those conjugate to their own inverses), and the series that are the composition of $n$ reversible series.
Keywords: Formal power series, involution, reversible, composition, group.
MSC 2000: Primary 20F99; Secondary 16W60.
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