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...

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...

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...

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...

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

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...

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...

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...

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

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...

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

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

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...

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...

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

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...

lemma Cantor's theorem Cantor–Bernstein–Schroeder theorem Cayley's formula Cayley's theorem Clique problem (to do) Compactness theorem (very compact proof)...

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,...

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...

subgroup of a permutation group, a result known today as Cayley's theorem. In succeeding years, Cayley systematically investigated infinite groups and the...

\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...

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

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...

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...