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For a Galois extension field K of a field F, the fundamental theorem of Galois theory states that the subgroups of the Galois group G=Gal(K/F) correspond with the subfields ...

A prime link is a link that cannot be represented as a knot sum of other links. Doll and Hoste (1991) list polynomials for oriented links of nine or fewer crossings, and ...

The Barnes-Wall lattice is a d-dimensional lattice that exists when d is a power of 2. It is implemented in the Wolfram Language as LatticeData[{"BarnesWall", n}]. Special ...

A group or other algebraic object is said to be Abelian (sometimes written in lower case, i.e., "abelian") if the law of commutativity always holds. The term is named after ...

An algebraic equation is algebraically solvable iff its group is solvable. In order that an irreducible equation of prime degree be solvable by radicals, it is necessary and ...

Gauge theory studies principal bundle connections, called gauge fields, on a principal bundle. These connections correspond to fields, in physics, such as an electromagnetic ...

The direct limit of the cohomology groups with coefficients in an Abelian group of certain coverings of a topological space.

This statement seems incomplete. Locate a reference and complete statement of the condition. For any group of k men out of N, there must be at least k jobs for which they are ...

Any locally compact Hausdorff topological group has a unique (up to scalars) nonzero left invariant measure which is finite on compact sets. If the group is Abelian or ...

A representation phi of a group G is faithful if it is one-to-one, i.e., if phi(g)=phi(h) implies g=h for g,h in G. Equivalently, phi is faithful if phi(g)=I_n implies g=e, ...