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...

{\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...

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...

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

(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...

{\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...

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...

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

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....

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...

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

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...

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...

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...

simple groups A100 and SL20(2) are far larger but easy to calculate with as they have "small" permutation or linear representations. Alternating groups, such...

In group theory, the Tits group 2F4(2)′, named for Jacques Tits (French: [tits]), is a finite simple group of order    211 · 33 · 52 · 13 = 17,971,200...

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...

The Poincaré group, named after Henri Poincaré (1905), was first defined by Hermann Minkowski (1908) as the isometry group of Minkowski spacetime. It...

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...

element of G ∗ H is an alternating product of powers of x with powers of y. In this case, G ∗ H is isomorphic to the free group generated by x and y. Suppose...

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

In geometry and group theory, a lattice in the real coordinate space R n {\displaystyle \mathbb {R} ^{n}} is an infinite set of points in this space with...

subgroup of the alternating group A4 is the Klein four group. The commutator subgroup of the symmetric group Sn is the alternating group An. The commutator...