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The dimension d of any irreducible representation of a group G must be a divisor of the index of each maximal normal Abelian subgroup of G. Note that while Itô's theorem was ...

The special orthogonal group SO_n(q) is the subgroup of the elements of general orthogonal group GO_n(q) with determinant 1. SO_3 (often written SO(3)) is the rotation group ...

A simple group is a group whose only normal subgroups are the trivial subgroup of order one and the improper subgroup consisting of the entire original group. Simple groups ...

Conjugation is the process of taking a complex conjugate of a complex number, complex matrix, etc., or of performing a conjugation move on a knot. Conjugation also has a ...

A quaternion Kähler manifold is a Riemannian manifold of dimension 4n, n>=2, whose holonomy is, up to conjugacy, a subgroup of Sp(n)Sp(1)=Sp(n)×Sp(1)/Z_2, but is not a ...

The general unitary group GU_n(q) is the subgroup of all elements of the general linear group GL(q^2) that fix a given nonsingular Hermitian form. This is equivalent, in the ...

In a noncommutative ring R, a left ideal is a subset I which is an additive subgroup of R and such that for all r in R and all a in I, ra in I. A left ideal of R can be ...

In the classical quasithin case of the quasithin theorem, if a group G does not have a "strongly embedded" subgroup, then G is a group of Lie-type in characteristic 2 of Lie ...

The centralizer of an element z of a group G is the set of elements of G which commute with z, C_G(z)={x in G,xz=zx}. Likewise, the centralizer of a subgroup H of a group G ...

A group representation of a group G on a vector space V can be restricted to a subgroup H. For example, the symmetric group on three letters has a representation phi on R^2 ...