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An alternating group is a subgroup of a symmetric group consisting of the even permutations.
The alternating group is to the symmetric group as the special orthogonal group is to the orthogonal group . See also at symmetric group – Whitehead tower
The alternating group on four elements is isomorphic to the orientation-preserving tetrahedral group.
The alternating group on five elements, of order , is the smallest nonabelian simple group. Geometrically, it may be realized as finite subgroup of SO(3) which carries a regular icosahedron into itself: the icosahedral group.
For all , the alternating group is simple. This is true even if is infinite: define for any set to consist of all permutations of each of which fixes all but finitely elements, and which is an even permutation on that finite subset.
Last revised on September 11, 2018 at 18:34:46. See the history of this page for a list of all contributions to it.