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A group $G= \langle t,a,| t^4=1, (t^{-1}at)^{-1} a (t^{-1}a t)= a^2 \rangle$ ( I do not remember the reference) was shown as a non -residually finite group. I do not know how to prove it. I will be thankfull for any hints.

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    $\begingroup$ This is just Higman's group semidirect cyclic-4. $\endgroup$
    – YCor
    Commented Oct 9, 2023 at 8:29

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