G. Frobenius. Suppose G is a Frobenius group consisting of permutations of a set X. A subgroup H of G fixing a point of X is called a Frobenius complement...

objects in modern mathematical physics, known as Frobenius manifolds. Ferdinand Georg Frobenius was born on 26 October 1849 in Charlottenburg, a suburb...

endomorphism Frobenius inner product Frobenius norm Frobenius method Frobenius group Frobenius theorem (differential topology) Georg Ludwig Frobenius (1566–1645)...

a Frobenius group Fp(p−1) (especially for p = 5), and is the affine general linear group, AGL(1, p). The Sylow p-subgroups of the symmetric group of...

was the Frobenius automorphism. He found that if a finite field of characteristic 2 also has an automorphism whose square was the Frobenius map, then...

mathematics contains the finite groups of small order up to group isomorphism. For n = 1, 2, … the number of nonisomorphic groups of order n is 1, 1, 1, 2,...

In mathematics, the Klein four-group is an abelian group with four elements, in which each element is self-inverse (composing it with itself produces...

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...

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

finite group is the number of its elements. If a group is not finite, one says that its order is infinite. The order of an element of a group (also called...

point group, Schoenflies notation Discrete group Euclidean group Even and odd permutations Frieze group Frobenius group Fuchsian group Geometric group theory...

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

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

invariants. The theory had been first developed in the 1879 paper of Georg Frobenius and Ludwig Stickelberger and later was both simplified and generalized...

as Frobenius morphism, Frobenius map) Frobenius determinant theorem Frobenius formula Frobenius group Frobenius complement Frobenius kernel Frobenius inner...

cyclic group of order q. In the case of O–(2n, q), the above x and y are conjugate, and are therefore the image of each other by the Frobenius automorphism...

In mathematics, a permutation group is a group G whose elements are permutations of a given set M and whose group operation is the composition of permutations...

In mathematics and group theory, the term multiplicative group refers to one of the following concepts: the group under multiplication of the invertible...

In mathematics, a Lie group (pronounced /liː/ LEE) is a group that is also a differentiable manifold, such that group multiplication and taking inverses...

In the mathematical field of group theory, Lagrange's theorem states that if H is a subgroup of any finite group G, then |H| is a divisor of |G|, i.e...

q {\displaystyle \alpha \colon x\mapsto x^{q}} (the rth power of the Frobenius automorphism). This allows one to define a Hermitian form on an Fq2 vector...

A quotient group or factor group is a mathematical group obtained by aggregating similar elements of a larger group using an equivalence relation that...

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...

specifically in the field of group theory, a solvable group or soluble group is a group that can be constructed from abelian groups using extensions. Equivalently...

In mathematics, topological groups are the combination of groups and topological spaces, i.e. they are groups and topological spaces at the same time...

mathematics, and specifically in group theory, a non-abelian group, sometimes called a non-commutative group, is a group (G, ∗) in which there exists at...

subgroups are of "Frobenius type", a slight generalization of Frobenius group, and in fact later on in the proof are shown to be Frobenius groups. They have...

an abstract group, and to say that one has a group action of the abstract group that consists of performing the transformations of the group of transformations...

{\displaystyle a\cdot b=1\ast \phi ^{-1}(a)\phi ^{-1}(b)} . A Frobenius group can be defined as a finite group of the form A ⋊ M {\displaystyle A\rtimes M} where...