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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 ...

A group of sociable numbers of order 3.

In a monoid or multiplicative group where the operation is a product ·, the multiplicative inverse of any element g is the element g^(-1) such that g·g^(-1)=g^(-1)·g=1, with ...

The identity element of an additive monoid or group or of any other algebraic structure (e.g., ring, module, abstract vector space, algebra) equipped with an addition. It is ...

Cohomology is an invariant of a topological space, formally "dual" to homology, and so it detects "holes" in a space. Cohomology has more algebraic structure than homology, ...

Given a number field K, there exists a unique maximal unramified Abelian extension L of K which contains all other unramified Abelian extensions of K. This finite field ...

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 trace of an n×n square matrix A is defined to be Tr(A)=sum_(i=1)^na_(ii), (1) i.e., the sum of the diagonal elements. The matrix trace is implemented in the Wolfram ...

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