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Suppose that V is a group representation of G, and W is a group representation of H. Then the vector space tensor product V tensor W is a group representation of the group ...

The restricted topological group direct product of the group G_(k_nu) with distinct invariant open subgroups G_(0_nu).

A group G is a finite or infinite set of elements together with a binary operation (called the group operation) that together satisfy the four fundamental properties of ...

A group G is nilpotent if the upper central sequence 1=Z_0<=Z_1<=Z_2<=...<=Z_n<=... of the group terminates with Z_n=G for some n. Nilpotent groups have the property that ...

A Cartesian product equipped with a "product topology" is called a product space (or product topological space, or direct product).

Direct sums are defined for a number of different sorts of mathematical objects, including subspaces, matrices, modules, and groups. The matrix direct sum is defined by ...

The direct sum of modules A and B is the module A direct sum B={a direct sum b|a in A,b in B}, (1) where all algebraic operations are defined componentwise. In particular, ...

The icosahedral group I_h is the group of symmetries of the icosahedron and dodecahedron having order 120, equivalent to the group direct product A_5×Z_2 of the alternating ...

The Cartesian product of two sets A and B (also called the product set, set direct product, or cross product) is defined to be the set of all points (a,b) where a in A and b ...

A free Abelian group is a group G with a subset which generates the group G with the only relation being ab=ba. That is, it has no group torsion. All such groups are a direct ...