Quotient groups and subgroups together form a way of describing every group by its presentation: any group is the quotient of the free group over the generators of the group, quotiented by the subgroup of relations. The dihedral group D4, for example, can be generated by two elements r and f (for example, r = r1, the right rotation and f = fv the vertical (or any other) reflection), which means that every symmetry of the square is a finite composition of these two symmetries or their inverses. Together with the relations COUNT 3
QSN1 What groups can be combined to describe every group? ANS1 is the quotient of the free group over the generators of the group QSN2 What group can be the quotient of the free group over the generators of the group? ANS2 any group QSN3 What is a finite composition of two symmetries or their inverses? ANS3 every symmetry of the square