Noun
alternating group (plural alternating groups)
(group theory) a group of even permutations of a finite set
A second straightforward construction of the icosahedron uses representation theory of the alternating group A 5 acting by direct isometries on the icosahedron. Source: Internet
In this case the alternating group agrees with the symmetric group, rather than being an index 2 subgroup, and the sign map is trivial. Source: Internet
The action of the symmetric group on a set with n elements is always n-transitive; the action of the alternating group is n-2-transitive. Source: Internet
The symmetric group on an infinite set does not have an associated alternating group: not all elements can be written as a (finite) product of transpositions. Source: Internet