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The set of elements g of a group such that g^(-1)Hg=H, is said to be the normalizer N_G(H) with respect to a subset of group elements H. If H is a subgroup of G, N_G(H) is ...

In the plane, there are 17 lattice groups, eight of which are pure translation. In R^3, there are 32 point groups and 230 space groups. In R^4, there are 4783 space lattice ...

The residue classes of a function f(x) mod n are all possible values of the residue f(x) (mod n). For example, the residue classes of x^2 (mod 6) are {0,1,3,4}, since 0^2=0 ...

An element of an adèle group, sometimes called a repartition in older literature (e.g., Chevalley 1951, p. 25). Adèles arise in both number fields and function fields. The ...

The disdyakis dodecahedral graph is Archimedean dual graph which is the skeleton of the disdyakis dodecahedron. It is implemented in the Wolfram Language as ...

For elliptic curves over the rationals Q, the group of rational points is always finitely generated (i.e., there always exists a finite set of group generators). This theorem ...

In graph theory, a cycle graph C_n, sometimes simply known as an n-cycle (Pemmaraju and Skiena 2003, p. 248), is a graph on n nodes containing a single cycle through all ...

The triakis tetrahedral graph is Archimedean dual graph which is the skeleton of the triakis tetrahedron. It is implemented in the Wolfram Language as ...

One or both of the square bracket symbols [ and ] are used in many different contexts in mathematics. 1. Square brackets are occasionally used in especially complex ...

A rooted graph is a graph in which one node is labeled in a special way so as to distinguish it from other nodes. The special node is called the root of the graph. The rooted ...