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Fixed points of analytic actions of supersoluble Lie groups on compact surfaces.


It is shown that every real analytic action of a connected supersoluble Lie group on a compact surface with nonzero Euler characteristic has a fixed point. This implies that E. Lima's fixed point free action of the affine group of the line on the 2-sphere S cannot be approximated by analytic actions. An example is given of an analytic, fixed point free action on S of a solvable group that is notsupersoluble.

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