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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.

Transitivity is a result of the symmetry in the group. A group G is called transitive if its group action (understood to be a subgroup of a permutation group on a set Omega) ...

For every module M over a unit ring R, the tensor product functor - tensor _RM is a covariant functor from the category of R-modules to itself. It maps every R-module N to N ...

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 ...

Let (X,A,mu) and (Y,B,nu) be measure spaces, let R be the collection of all measurable rectangles contained in X×Y, and let lambda be the premeasure defined on R by ...

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 ...

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