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.

From New York Times

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.

From Project Gutenberg

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

From Project Gutenberg

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.

From Project Gutenberg

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.

From New York Times