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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.

A group G such that the quotient group G/Z(G), where Z(G) is the group center of G, is Abelian. An equivalent condition is that the commutator subgroup G^' is contained in ...

A permutation group in which the permutations are limited to transpositions.

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 ...

An Abelian group is a group for which the elements commute (i.e., AB=BA for all elements A and B). Abelian groups therefore correspond to groups with symmetric multiplication ...

A group which is related to the Taniyama-Shimura conjecture.

One of the symmetry groups of the Platonic solids. There are three polyhedral groups: the tetrahedral group of order 12, the octahedral group of order 24, and the icosahedral ...

A group G is said to act on a set X when there is a map phi:G×X->X such that the following conditions hold for all elements x in X. 1. phi(e,x)=x where e is the identity ...