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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).

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

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 ...

The Ree group R(q) is the automorphism group of a S(2,q+1,q^3+1) Steiner system.

The free part of the homology group with a domain of coefficients in the group of integers (if this homology group is finitely generated).

The center of a group is the set of elements which commute with every element of the group. It is equal to the intersection of the centralizers of the group elements.