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China has expressed frustration that the United States has not established a clear point person in the negotiations, which have been led by an alternating group of officials including Steven Mnuchin, the Treasury secretary; Robert E. Lighthizer, the United States trade representative; Mr. Ross; and others.

Those permutations which leave the product unaltered constitute a group of order n!/2, which is called the alternating group of degree n; it is a self-conjugate subgroup of the symmetric group.

Except when n = 4 the alternating group is a simple group.

A group of degree n, which is not contained in the alternating group, must necessarily have a self-conjugate subgroup of index 2, consisting of those of its permutations which belong to the alternating group.

The alternating group sections in “Crisis Variations” are rougher and more interesting than those of the other works: floorbound dancers are towed under by the rolling of other floorbound dancers.