On Groups Generated by the Squares
نویسندگان
چکیده
It was known that the quaternion group and the octic group could not be generated by the squares of any group [5, pp. 193-194]. A natural question is which groups are generated by the squares of some groups. Clearly, groups of odd order and simple groups are generated by their own squares. In this paper, we show in a concrete manner that abelian groups are generated by the squares of some groups, and we show that every group is contained in the set of squares of some group. We give conditions for the dihedral and dicyclic groups to be generated by the squares of some groups. Also we show that several classes of nonabelian 2-groups cannot be generated by the squares of any group.
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