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A group or other algebraic object is said to be Abelian (sometimes written in lower case, i.e., "abelian") if the law of commutativity always holds. The term is named after ...

Let M(X) denote the group of all invertible maps X->X and let G be any group. A homomorphism theta:G->M(X) is called an action of G on X. Therefore, theta satisfies 1. For ...

The identity element of an additive group G, usually denoted 0. In the additive group of vectors, the additive identity is the zero vector 0, in the additive group of ...

Given an acute angle in a right triangle, the adjacent side is the leg of the triangle from which the angle to the hypotenuse is measured. Lengths of adjacent and opposite ...

The vertex of an isosceles triangle having angle different from the two equal angles is called the apex of the isosceles triangle. The common polygon vertex at the top of a ...

Suppose that E(G) (the commuting product of all components of G) is simple and G contains a semisimple group involution. Then there is some semisimple group involution x such ...

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 ...

The cokernel of a group homomorphism f:A-->B of Abelian groups (modules, or abstract vector spaces) is the quotient group (quotient module or quotient space, respectively) ...

A group L is a component of H if L is a quasisimple group which is a subnormal subgroup of H.

Let L be a link in R^3 and let there be a disk D in the link complement R^3-L. Then a surface F such that D intersects F exactly in its boundary and its boundary does not ...