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A discrete group is a topological group with the discrete topology. Often in practice, discrete groups arise as discrete subgroups of continuous Lie groups acting on a ...

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 ...

The first group isomorphism theorem, also known as the fundamental homomorphism theorem, states that if phi:G->H is a group homomorphism, then Ker(phi)⊴G and ...

Let G be a subgroup of the modular group Gamma. Then an open subset R_G of the upper half-plane H is called a fundamental region of G if 1. No two distinct points of R_G are ...

The natural projection, also called the homomorphism, is a logical way of mapping an algebraic structure onto its quotient structures. The natural projection pi is defined ...

A projective space is a space that is invariant under the group G of all general linear homogeneous transformation in the space concerned, but not under all the ...

Given a ring R with identity, the special linear group SL_n(R) is the group of n×n matrices with elements in R and determinant 1. The special linear group SL_n(q), where q is ...

Every semisimple Lie algebra g is classified by its Dynkin diagram. A Dynkin diagram is a graph with a few different kinds of possible edges. The connected components of the ...

Let E be a Euclidean space, (beta,alpha) be the dot product, and denote the reflection in the hyperplane P_alpha={beta in E|(beta,alpha)=0} by ...

The Steenrod algebra has to do with the cohomology operations in singular cohomology with integer mod 2 coefficients. For every n in Z and i in {0,1,2,3,...} there are ...