A question of Mazurov on groups of exponent dividing 12

Abstract

Mazurov asked whether a group of exponent dividing 12, which is generated by x, y and z subject to the relations $x^3=y^2=z^2={\left(xy\right)}^3={\left(yz\right)}^3=1,$ has order at most 12. We show that if such a group is finite, then the answer is yes.

Keywords: 20D60; 20F05; Exponent; finite presentation; groups.