In mathematics, specifically group theory, Frobenius's theorem states that if n divides the order of a finite group G, then the number of solutions of...

Perron–Frobenius theorem in matrix theory concerning the eigenvalues and eigenvectors of a matrix with positive real coefficients Frobenius's theorem (group...

called the Frobenius kernel K. (This is a theorem due to Frobenius (1901); there is still no proof of this theorem that does not use character theory, although...

In the mathematical field of group theory, Lagrange's theorem states that if H is a subgroup of any finite group G, then | H | {\displaystyle |H|} is...

In matrix theory, the Perron–Frobenius theorem, proved by Oskar Perron (1907) and Georg Frobenius (1912), asserts that a real square matrix with positive...

In mathematics, specifically group theory, Cauchy's theorem states that if G is a finite group and p is a prime number dividing the order of G (the number...

differential equations, number theory, and to group theory. He is known for the famous determinantal identities, known as Frobenius–Stickelberger formulae, governing...

mathematics, the Frobenius determinant theorem was a conjecture made in 1896 by the mathematician Richard Dedekind, who wrote a letter to F. G. Frobenius about it...

called Burnside's counting theorem, the Cauchy–Frobenius lemma, or the orbit-counting theorem, is a result in group theory that is often useful in taking...

mathematics, the Peter–Weyl theorem is a basic result in the theory of harmonic analysis, applying to topological groups that are compact, but are not...

In mathematics, and in particular representation theory, Frobenius reciprocity is a theorem expressing a duality between the process of restricting and...

as an example of the group action of G on the elements of G. Burnside's theorem in group theory states that if G is a finite group of order paqb, where...

In number theory, Fermat's little theorem states that if p is a prime number, then for any integer a, the number ap − a is an integer multiple of p. In...

history and credit for the fundamental theorem is complicated by the fact that it was proven when group theory was not well-established, and thus early...

of finite simple groups (popularly called the enormous theorem) is a result of group theory stating that every finite simple group is either cyclic,...

theorem. Otto Schreier published an algebraic proof of this result in 1927, and Kurt Reidemeister included a comprehensive treatment of free groups in...

theorem (geometric group theory) Focal subgroup theorem (abstract algebra) Frobenius determinant theorem (group theory) Frobenius reciprocity theorem...

such as Galois theory, invariant theory, the representation theory of Lie groups, and combinatorics. Cayley's theorem states that every group G {\displaystyle...

Cartan's theorem. The quotient of a Lie group by a closed normal subgroup is a Lie group. The universal cover of a connected Lie group is a Lie group. For...

Brauer developed a powerful theory of characters in this case as well. Many deep theorems on the structure of finite groups use characters of modular representations...

The Chebotarev density theorem in algebraic number theory describes statistically the splitting of primes in a given Galois extension K of the field Q...

subgroup of a Hausdorff commutative topological group is closed. The isomorphism theorems from ordinary group theory are not always true in the topological setting...

Cambridge University Press, Theorem 14.14, p. 401, ISBN 978-0-521-47465-8 Ore, Øystein (1938), "Structures and group theory. II", Duke Mathematical Journal...

In commutative algebra and field theory, the Frobenius endomorphism (after Ferdinand Georg Frobenius) is a special endomorphism of commutative rings with...

mathematics, specifically in group theory, the phrase group of Lie type usually refers to finite groups that are closely related to the group of rational points...

In abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known...

case of dimension two. The Cartan–Dieudonné theorem is the generalization of this result to the orthogonal group of a nondegenerate quadratic form over a...

any 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...

In mathematics, the Feit–Thompson theorem, or odd order theorem, states that every finite group of odd order is solvable. It was proved in the early 1960s...

abelian group underlies many fundamental algebraic structures, such as fields, rings, vector spaces, and algebras. The theory of abelian groups is generally...