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A homogeneous space M is a space with a transitive group action by a Lie group. Because a transitive group action implies that there is only one group orbit, M is isomorphic ...

Many algorithms have been devised for determining the prime factors of a given number (a process called prime factorization). They vary quite a bit in sophistication and ...

Gives a lower bound for the inner product (Lu,u), where L is a linear elliptic real differential operator of order m, and u has compact support.

A group of sociable numbers of order 3.

A group action G×X->X is called free if, for all x in X, gx=x implies g=I (i.e., only the identity element fixes any x). In other words, G×X->X is free if the map G×X->X×X ...

An orthogonal transformation is a linear transformation T:V->V which preserves a symmetric inner product. In particular, an orthogonal transformation (technically, an ...

The geometry of the Lie group consisting of real matrices of the form [1 x y; 0 1 z; 0 0 1], i.e., the Heisenberg group.

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 ...

The intersection phi(G) of all maximal subgroups of a given group G.

A brute-force method of finding a divisor of an integer n by simply plugging in one or a set of integers and seeing if they divide n. Repeated application of trial division ...