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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.

A map x|->x^p where p is a prime.

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.

Let F be a field of field characteristic p. Then the Frobenius automorphism on F is the map phi:F->F which maps alpha to alpha^p for each element alpha of F.