7.3 (1980)

Prove that the periodic product of odd exponent $n \geqslant 665$ of non-trivial groups $F_1, \dots, F_k$ which do not contain involutions cannot be generated by less than $k$ elements. This would imply, on the basis of (S. I. Adian, Sov. Math. Doklady, 19, (1978), 910–913), the existence of $k$-generated simple groups which cannot be generated by less than $k$ elements, for any $k > 0$.