Let $G$ be a group which is generated by the set of its involutions, and assume that the product of every two involutions in $G$ has order a power of 2. Is it possible that $G$ has an element of odd order $\neq 1$?
Can a group generated by its involutions the product of every two of which has order a power of 2 have an element of odd order?
Stefan Kohl ♦
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