Search Results for ""

If two groups are residual to a third, every group residual to one is residual to the other. The Gambier extension of this theorem states that if two groups are ...

A map psi:M->M, where M is a manifold, is a finite-to-one factor of a map Psi:X->X if there exists a continuous surjective map pi:X->M such that psi degreespi=pi degreesPsi ...

A set function mu is finitely additive if, given any finite disjoint collection of sets {E_k}_(k=1)^n on which mu is defined, mu( union _(k=1)^nE_k)=sum_(k=1)^nmu(E_k).

Given two groups G and H, there are several ways to form a new group. The simplest is the direct product, denoted G×H. As a set, the group direct product is the Cartesian ...

A set function mu is said to possess finite subadditivity if, given any finite disjoint collection of sets {E_k}_(k=1)^n on which mu is defined, mu( union ...

Every finite simple group (that is not cyclic) has even group order, and the group order of every finite simple noncommutative group is doubly even, i.e., divisible by 4 ...

Let X be a set and S a collection of subsets of X. A set function mu:S->[0,infty] is said to possess finite monotonicity provided that, whenever a set E in S is covered by a ...

A simplicial complex K is said to be locally finite if each vertex of K belongs only to finitely many simplices of K.

On a Riemannian manifold M, tangent vectors can be moved along a path by parallel transport, which preserves vector addition and scalar multiplication. So a closed loop at a ...

The quotient space K^__1A=K_1A/{0,[-1]} of the Whitehead group K_1A is known as the reduced Whitehead group. Here, the element [-1] in K_1A denotes the order-2 element ...