In the mathematical discipline of group theory, Cayley's theorem, named in honour of Arthur Cayley, states that every group G is isomorphic to a subgroup...

In linear algebra, the Cayley–Hamilton theorem (named after the mathematicians Arthur Cayley and William Rowan Hamilton) states that every square matrix...

denoted by Sn, and may be called the symmetric group on n letters. By Cayley's theorem, every group is isomorphic to some permutation group. The way in which...

structure of a group. Its definition is suggested by Cayley's theorem (named after Arthur Cayley), and uses a specified set of generators for the group...

many subgroups of a given order are contained in G. Cayley's theorem, named in honour of Arthur Cayley, states that every group G is isomorphic to a subgroup...

theory, Cayley tables, Cayley graphs, and Cayley's theorem are named in his honour, as well as Cayley's formula in combinatorics. Arthur Cayley was born...

type morphisms into a fixed object. It is a vast generalisation of Cayley's theorem from group theory (viewing a group as a miniature category with just...

theory, the representation theory of Lie groups, and combinatorics. Cayley's theorem states that every group G {\displaystyle G} is isomorphic to a subgroup...

on itself by left multiplication is free. This observation implies Cayley's theorem that any group can be embedded in a symmetric group (which is infinite...

properties is isomorphic to another (abstract or concrete) structure. Cayley's theorem states that every group is isomorphic to a permutation group. Representation...

semigroup have the same action, then they are equal. An analogue of Cayley's theorem shows that any semigroup can be realized as a transformation semigroup...

Kirchhoff's theorem is a generalization of Cayley's formula which provides the number of spanning trees in a complete graph. Kirchhoff's theorem relies on...

one may proceed as follows. Choose a field K and a finite group G. Cayley's theorem says that G is (up to isomorphism) a subgroup of the symmetric group...

called the composition group. A fundamental result in group theory, Cayley's theorem, essentially says that any group is in fact just a subgroup of a symmetric...

In mathematics, the Cayley–Bacharach theorem is a statement about cubic curves (plane curves of degree three) in the projective plane P2. The original...

order (just as every group is isomorphic to a permutation group – see Cayley's theorem). To see this, associate to each element x of X the set X ≤ ( x ) =...

is linear, because it can be realized by permutation matrices using Cayley's theorem. Among infinite groups, linear groups form an interesting and tractable...

groups) Burnside's theorem (group theory) Cartan–Dieudonné theorem (group theory) Cauchy's theorem (finite groups) Cayley's theorem (group theory)...

semigroups was the Wagner–Preston Theorem, which is an analogue of Cayley's theorem for groups: Wagner–Preston Theorem. If S is an inverse semigroup, then...

substituted in Cayley's resolvent, the resulting sextic polynomial has a rational root, which can be easily tested for using the rational root theorem. Around...

linked to the more general notion of a semigroup by an analogue of Cayley's theorem. (A note on terminology: the terminology used in this area varies,...

semigroups began in the early 20th century. Early results include a Cayley theorem for semigroups realizing any semigroup as a transformation semigroup...

coniques. Par B. P." Pascal's theorem is a special case of the Cayley–Bacharach theorem. A degenerate case of Pascal's theorem (four points) is interesting;...

\mathbb {Z} _{3}=\mathbb {Z} \,/\,3\mathbb {Z} _{3}} is cyclic. Via Cayley's theorem, Z 3 {\displaystyle \mathbb {Z} _{3}} is isomorphic to a subgroup of...

In mathematics, Cayley's formula is a result in graph theory named after Arthur Cayley. It states that for every positive integer n {\displaystyle n} ...

the Cayley–Dickson construction takes any algebra with involution to another algebra with involution of twice the dimension.: 45  Hurwitz's theorem states...

Zariski-closed, subgroup of some G L n {\displaystyle \mathrm {GL} _{n}} by Cayley's theorem). In addition it is both affine and projective. Thus, in particular...

formula Cayley's hyperdeterminant Cayley's mousetrap — a card game Cayley's nodal cubic surface Cayley normal 2-complement theorem Cayley's ruled cubic...

is the symmetry group of its Cayley graph; the free group is the symmetry group of an infinite tree graph. Cayley's theorem states that any abstract group...

generalisation of upper sets in posets, and Yoneda's representability theorem generalizes Cayley's theorem in group theory. Let C be a locally small category and let...