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The socle of a group G is the subgroup generated by its minimal normal subgroups. For example, the symmetric group S_4 has two nontrivial normal subgroups: A_4 and ...

The asymptotic series of the Airy function Ai(z) (and other similar functions) has a different form in different sectors of the complex plane.

The symmetric group S_n of degree n is the group of all permutations on n symbols. S_n is therefore a permutation group of order n! and contains as subgroups every group of ...

An irregular dodecahedron.

The tritangent of a cubic surface is a plane which intersects the surface in three mutually intersecting lines. Each intersection of two lines is then a tangent point of the ...

A cycle of a graph G, also called a circuit if the first vertex is not specified, is a subset of the edge set of G that forms a path such that the first node of the path ...

A generalized hexagon is a generalized polygon of order 6. GH(1,2) is more commonly known as the Heawood graph, but is also the (3,6)-cage graph, the cubic vertex-transitive ...

An edge-induced subgraph is a subset of the edges of a graph G together with any vertices that are their endpoints. The subgraph induced by a set of edges can be computed in ...

The finite group T is one of the three non-Abelian groups of order 12 (out of a total of fives groups of order 12), the other two being the alternating group A_4 and the ...

A tree decomposition is a mapping of a graph into a related tree with desirable properties that allow it to be used to efficiently compute certain properties (e.g., ...