1. Furthermore, we see that the even permutations form a subgroup of " S ". 2. The symmetries correspond to the even permutations of the body diagonals and the same combined with inversion. 3. In terms of permutations the two group elements of are the set of even permutations and the set of odd permutations. 4. In mathematics, an "'alternating group "'is the group of even permutations of a finite set. 5. In three dimensions only, the cyclic permutations of are all even permutations , similarly the anticyclic permutations are all odd permutations. 6. Only even permutations of the corner pieces are possible, so the number of possible arrangements of corner pieces is 6 ! / 2. 7. An odd permutation followed by an odd permutation will represent an overall even permutation ( adding two odd numbers always returns an even number ). 8. The even permutations produce the subgroup of permutation matrices of determinant + 1, the order " n " ! / 2 alternating group. 9. Similarly, the mirror image has either an odd permutation with an even number of plus signs or an even permutation with an odd number of plus signs. 10. That is, is 1 if is an even permutation of, " 1 if it is an odd permutation, and 0 if any index is repeated.
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