In the example above, the identity and the rotations constitute a subgroup R = {id, r1, r2, r3}, highlighted in red in the group table above: any two rotations composed are still a rotation, and a rotation can be undone by (i.e. is inverse to) the complementary rotations 270° for 90°, 180° for 180°, and 90° for 270° (note that rotation in the opposite direction is not defined). The subgroup test is a necessary and sufficient condition for a subset H of a group G to be a subgroup: it is sufficient to check that g−1h ∈ H for all elements g, h ∈ H. Knowing the subgroups is important in understanding the group as a whole.d[›]
In the example above , the identity and the rotations constitute a subgroup R = { i d , r1 , r2 , r3 } , highlighted in red in the group table above : any two rotations composed are still a rotation , and a rotation can be undone by ( i.e. is inverse to ) the complementary rotations 270 ° for 90 ° , 180 ° for 180 ° , and 90 ° for 270 ° ( note that rotation in the opposite direction is not defined ) . The subgroup test is a necessary and sufficient condition for a subset H of a group G to be a subgroup : it is sufficient to check that g−1h ∈ H for all elements g , h ∈ H. Knowing the subgroups is important in understanding the group as a whole.d[› ]
What is composed of two rotations?
What is composed of two rotations ?
a rotation
a rotation