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I want to know why are faithful actions called faithful and who first called them faithful?

Definition: An action $G$ on $X$ is faithful when ${g_1 \neq g_2 \Rightarrow g_1 x \neq g_2 x}$ for some ${x \in X}$ (different elements of $G$ act differently at some point).

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  • $\begingroup$ good question (+$1$); I always remembered faithful as reliable that no two group elements act the same on all set elements, otherwise there wouldn't be a reason to have two different group elements in the context of their action, but I don't really know $\endgroup$
    – J. W. Tanner
    Commented Apr 27, 2020 at 20:24
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    $\begingroup$ +1: good question, but you might do better on hsm.stackexchange.com $\endgroup$
    – Rob Arthan
    Commented Apr 27, 2020 at 21:51
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    $\begingroup$ Now posted to MO, mathoverflow.net/questions/359121/… $\endgroup$
    – Gerry Myerson
    Commented May 2, 2020 at 1:34
  • $\begingroup$ and in fact is comprehensively answered on MO, as per Gerry's link. $\endgroup$
    – postmortes
    Commented Sep 18, 2020 at 9:26

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