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...

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

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...

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

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

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...

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...

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...

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...

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...

{\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...

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....

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...

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...

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

finite simple group where the centralizer of some involution is isomorphic to the nontrivial central extension of the alternating group A11 of degree...

(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...

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...

quadratic form is also an alternating form. The spinor norm is a homomorphism from an orthogonal group over a field F to the quotient group F× / (F×)2 (the multiplicative...

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

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...

general group. Lie groups appear in symmetry groups in geometry, and also in the Standard Model of particle physics. The Poincaré group is a Lie group consisting...

mathematics, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not...

and the alternating group A5 of order 60, which is to say, the rotational icosahedral group. That was Janko's original conception of the group. In fact...

The smallest (non-trivial) perfect group is the alternating group A5. More generally, any non-abelian simple group is perfect since the commutator subgroup...

the even permutations. The alternating group is a non-abelian simple group for n ≥ 5 {\displaystyle n\geq 5} . Given a group G {\displaystyle G} and an...