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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[].

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.

The unitary group U_n(q) is the set of n×n unitary matrices.

The homeomorphism group of a topological space X is the set of all homeomorphisms f:X->X, which forms a group by composition.