Does the Tarski Monster group with prime 5 exist? I know that for 2 and 3, the group does not exist, but what about 5?

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    $\begingroup$ The Burnside problem en.wikipedia.org/wiki/Burnside's_problem for exponent 5 still seems to be open. $\endgroup$ – Primoz Aug 2 '13 at 7:23
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    $\begingroup$ It is an open problem. It is not even known whether finitely generated groups of exponent 5 are finite. $\endgroup$ – Derek Holt Aug 2 '13 at 7:26
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    $\begingroup$ Then in that case, i will try it. $\endgroup$ – D. N. Aug 2 '13 at 7:37
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    $\begingroup$ @Deibor: Good choice! Finding a Tarski monster for $p=5$ is the surest way to get a Fields medal. $\endgroup$ – Mark Sapir Aug 2 '13 at 7:56
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    $\begingroup$ Of course, you won't get a Fields medal even with a Tarski monster, if you are at least 40 years old on January 1st of the next year that is congruent to 2 mod 4. $\endgroup$ – S. Carnahan Aug 3 '13 at 8:05

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