The automorphism group of a restricted product over the projective plane P^2(k) acts decently, meaning subgroups with finite orbits or pointwise fixed points have global fixed points.
Locally elliptic actions, torsion groups, and nonpositively curved spaces
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Decent actions of groups on restricted products
The automorphism group of a restricted product over the projective plane P^2(k) acts decently, meaning subgroups with finite orbits or pointwise fixed points have global fixed points.