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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 ...

A group in which the elements are square matrices, the group multiplication law is matrix multiplication, and the group inverse is simply the matrix inverse. Every matrix ...

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).

Coordinates useful for plotting projective three-dimensional curves of the form f(x_0,x_1,x_2,x_3)=0 which are defined by x_0 = 1-z-sqrt(2)x (1) x_1 = 1-z+sqrt(2)x (2) x_2 = ...

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

The tetrahedral equation, by way of analogy with the icosahedral equation, is a set of related equations derived from the projective geometry of the octahedron. Consider a ...

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

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 ...

A rotation group is a group in which the elements are orthogonal matrices with determinant 1. In the case of three-dimensional space, the rotation group is known as the ...

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 ...