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Let N be a nilpotent, connected, simply connected Lie group, and let D be a discrete subgroup of N with compact right quotient space. Then N/D is called a nilmanifold.

In real and functional analysis, equicontinuity is a concept which extends the notion of uniform continuity from a single function to collection of functions. Given ...

The Killing form is an inner product on a finite dimensional Lie algebra g defined by B(X,Y)=Tr(ad(X)ad(Y)) (1) in the adjoint representation, where ad(X) is the adjoint ...

Consider a collection of diagonal matrices H_1,...,H_k, which span a subspace h. Then the ith eigenvalue, i.e., the ith entry along the diagonal, is a linear functional on h, ...

A formal mathematical theory which introduces "components at infinity" by defining a new type of divisor class group of integers of a number field. The divisor class group is ...

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 wreathed product of the monster group by Z_2. The bimonster is a quotient of the Coxeter group with the above Coxeter-Dynkin diagram. This had been conjectured by Conway, ...

The Janko groups are the four sporadic groups J_1, J_2, J_3 and J_4. The Janko group J_2 is also known as the Hall-Janko group. The Janko groups are implemented in the ...

An automorphism of a graph is a graph isomorphism with itself, i.e., a mapping from the vertices of the given graph G back to vertices of G such that the resulting graph is ...

A rational homomorphism phi:G->G^' defined over a field is called an isogeny when dimG=dimG^'. Two groups G and G^' are then called isogenous if there exists a third group ...