There is a theorem for finite groups of isometries in a plane which says that there is a point in the plane fixed by every element in the group (theorem 6.4.7 in Algebra - M Artin). While the proof itself is fairly simple to understand, there is an unstated belief that this is the only point that is fixed. Can somebody point me to a proof that there is only one point fixed by the group over all points in the plane? I would be so grateful,(adsbygoogle = window.adsbygoogle || []).push({});

Thanks,

Kind regards,

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SACHIN

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# Regarding fixed points in finite groups of isometries

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