The set of all cube moves generates the Rubik’s Cube group, which is a subgroup of one of these groups with degree 48. For 10 points each:
[10h] Name these groups that, when defined over sets of n symbols, consist of the n-factorial permutations of the n symbols.
ANSWER: symmetric groups [prompt on S-sub-n]
[10e] The Rubik’s Cube group has 81,120 equivalence classes of elements with this property. Another definition of this property holds for pairs of complex numbers with equal real parts and complex parts with opposite signs, like a plus b i and a minus b i.
ANSWER: conjugate [accept conjugacy classes or complex conjugates]
[10m] The Rubik’s Cube group is non-abelian, meaning that its operation lacks this property. For a binary relation, symmetry is analogous to this property for binary operations.
ANSWER: commutative property [or commutativity]
<Steven Yuan, Science - Math> ~20271~ <Editor: David Bass>