alternating group

American  

noun

Mathematics.

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

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Etymology

Origin of alternating group

First recorded in 1905–10

Example Sentences

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 Encyclopaedia Britannica, 11th Edition, Volume 12, Slice 6 "Groups, Theory of" to "Gwyniad" by Various

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 Encyclopaedia Britannica, 11th Edition, Volume 12, Slice 6 "Groups, Theory of" to "Gwyniad" by Various

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

From Encyclopaedia Britannica, 11th Edition, Volume 12, Slice 6 "Groups, Theory of" to "Gwyniad" by Various