No finite group of odd order has commuting probability 1/17; the proof uses a structural theorem making the Sylow p-subgroup normal and abelian when cp(G)=1/p.
On the commuting probability in finite groups
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The solution to Kourovka problem 21.88
No finite group of odd order has commuting probability 1/17; the proof uses a structural theorem making the Sylow p-subgroup normal and abelian when cp(G)=1/p.