Alternating group information

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

{\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 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):...

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

solvable, non-nilpotent group is the symmetric group S3. In fact, as the smallest simple non-abelian group is A5, (the alternating group of degree 5) it follows...

group can be studied using the properties of its action on the corresponding set. For example, in this way one proves that for n ≥ 5, the alternating...

5-transitive groups that are neither symmetric groups nor alternating groups (Cameron 1992, p. 139). The only 4-transitive groups are the symmetric groups Sk for...

groups states that every finite simple group is cyclic, or alternating, or in one of 16 families of groups of Lie type, or one of 26 sporadic groups....

five-dimensional irreducible representations. The representation theory of the alternating groups is similar, though the sign representation disappears. For n ≥ 7,...

the alternating group A5 agrees with the chiral icosahedral group (itself an exceptional object), and the double cover of the alternating group A5 is...

mathematics, a dihedral group is the group of symmetries of a regular polygon, which includes rotations and reflections. Dihedral groups are among the simplest...

symmetric group of X is transitive, in fact n-transitive for any n up to the cardinality of X. If X has cardinality n, the action of the alternating group is...

In abstract algebra, a cyclic group or monogenous group is a group, denoted Cn (also frequently Z {\displaystyle \mathbb {Z} } n or Zn, not to be confused...

other than the cyclic groups, the alternating groups, the Tits group, and the 26 sporadic simple groups. For any finite group G, the order (number of...

non-degenerate alternating form), unitary group, U(V), which, when F = C, preserves a non-degenerate hermitian form on V. These groups provide important...

has an alternating diagram. Many of the knots with crossing number less than 10 are alternating. This fact and useful properties of alternating knots,...

exception to this: the alternating group A6 has outer automorphism group of order 4, rather than 2 as do the other simple alternating groups (given by conjugation...

Each group (except those of cardinality 1 and 2) is represented by its Cayley table. Like each group, S4 is a subgroup of itself. The alternating group contains...

A quotient group or factor group is a mathematical group obtained by aggregating similar elements of a larger group using an equivalence relation that...

the alternating groups of degree at least 5, the infinite family of commutator groups 2F4(22n+1)′ of groups of Lie type (containing the Tits group), and...

In mathematics, a permutation group is a group G whose elements are permutations of a given set M and whose group operation is the composition of permutations...

In mathematics, given two groups, (G,∗) and (H, ·), a group homomorphism from (G,∗) to (H, ·) is a function h : G → H such that for all u and v in G it...

In mathematics, topological groups are the combination of groups and topological spaces, i.e. they are groups and topological spaces at the same time...

In mathematics, the free group FS over a given set S consists of all words that can be built from members of S, considering two words to be different...