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The set of all nonsingular affine transformations of a translation in space constitutes a group known as the affine group. The affine group contains the full linear group and ...

A particular type of automorphism group which exists only for groups. For a group G, the outer automorphism group is the quotient group Aut(G)/Inn(G), which is the ...

An element of order 2 in a group (i.e., an element A of a group such that A^2=I, where I is the identity element).

A continuous group G which has the topology of a T2-space is a topological group. The simplest example is the group of real numbers under addition. The homeomorphism group of ...

A presentation of a group is a description of a set I and a subset R of the free group F(I) generated by I, written <(x_i)_(i in I)|(r)_(r in R)>, where r=1 (the identity ...

The Tits group is a group of order 17971200. It is implemented in the Wolfram Language as TitsGroupT[].

A primitive group action is transitive and it has no nontrivial group blocks. A transitive group action that is not primitive is called imprimitive. A group that has a ...

The singleton set {0}, with respect to the trivial group structure defined by the addition 0+0=0. The element 0 is the additive identity element of the group, and also the ...

The image of A_5×A_5 in the special orthogonal group SO(4), where A_5 is the icosahedral group.

The group of rotations and translations.