an alternating group is the group of even permutations of a finite set. The alternating group on a set of n elements is called the alternating group of...

square to zero Alternating form, a function formula in algebra Alternating group, the group of even permutations of a finite set Alternating knot, a knot...

does not change the homology of the symmetric group; the alternating group phenomena do yield symmetric group phenomena – the map A 4 ↠ C 3 {\displaystyle...

In the mathematical area of group theory, the covering groups of the alternating and symmetric groups are groups that are used to understand the projective...

between projective special linear groups and alternating groups (these groups are all simple, as the alternating group over 5 or more letters is simple):...

{\displaystyle A_{n}} – alternating group for n ≥ 5 {\displaystyle n\geq 5} The alternating groups may be considered as groups of Lie type over the field...

In group theory, a branch of mathematics, the automorphisms and outer automorphisms of the symmetric groups and alternating groups are both standard examples...

alternating groups also have exceptional properties. The alternating groups usually have an outer automorphism group of order 2, but the alternating group...

{\displaystyle V} is a normal subgroup of the alternating group A 4 {\displaystyle A_{4}} (and also the symmetric group S 4 {\displaystyle S_{4}} ) on four letters...

(the alternating group of degree 4), which has 12 elements but no subgroup of order 6. A "Converse of Lagrange's Theorem" (CLT) group is a finite group with...