For every positive rational number q, we find a free group of rotations of rank 2 acting on (√q𝕊²) ∩ ℚ³ whose all elements distinct from the identity have no fixed point.
@article{bwmeta1.element.bwnjournal-article-aav85i2p135bwm,
author = {Kenzi Sat\^o},
title = {Free groups acting without fixed points on rational spheres},
journal = {Acta Arithmetica},
volume = {84},
year = {1998},
pages = {135-140},
zbl = {0986.20029},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav85i2p135bwm}
}
Kenzi Satô. Free groups acting without fixed points on rational spheres. Acta Arithmetica, Tome 84 (1998) pp. 135-140. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav85i2p135bwm/
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