alternating group

noun

Mathematics.

1. the subgroup consisting of all even permutations, of the group of all permutations of a finite set.

Word History and Origins

Origin of alternating group¹

First recorded in 1905–10

Example Sentences

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.

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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.

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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.

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

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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.

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