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The Lefschetz number of self-maps of Lie groups. (English) Zbl 0689.55005
Summary: In this note we present a simple approach to the Lefschetz number for the self-maps of Lie groups. As an application it is proved that for any map f: $$G\to G$$ of a compact connected Lie group G, there is a solution to $$(f(x))^ k=x$$ for some $$k\leq \lambda +1$$, where $$\lambda$$ is the rank of the group G.

##### MSC:
 55M20 Fixed points and coincidences in algebraic topology
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