Can we find a specific example of a group where two of its element has order 3 but its product has order five.
The question here possible order of product of two elements says that there exists such group.
But can someone find a specific example?
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Particularly relevant is Dietrich Burde's answer to linked question and the comment exchange. – pjs36 Feb 27 '16 at 18:55
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thanx, i missed those comments – Babai Feb 27 '16 at 18:58
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1The proof of Theorem $1.64$ in Milne's lecture notes gives "a specific example". Milne constructs elements $a$ and $b$ of arbitrary order $m,n>1$ in the group $PSL_2(\mathbb{F}_q)$ for a suitable prime power $q$, such that $ab$ has arbitrary order $r>1$. – Dietrich Burde Feb 27 '16 at 19:12
