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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 ...

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 ...

The Fischer groups are the three sporadic groups Fi_(22), Fi_(23), and Fi_(24)^'. These groups were discovered during the investigation of 3-transposition groups. The Fischer ...

A folding function is a function that maps the integers Z={...,-3,-2,-1,0,1,2,3,...} onto the nonnegative integers Z^*={0,1,2,3,...}. This type of function arises naturally ...

The fourth group isomorphism theorem, also called the lattice group isomorphism theorem, lets G be a group and let N⊴G, where N⊴G indicates that N is a normal subgroup of G. ...

Let R be a ring, and let I be an ideal of R. The correspondence A<->A/I is an inclusion preserving bijection between the set of subrings A of R that contain I and the set of ...

Given an infinitive sequence {x_n} with associative array a(i,j), then {x_n} is said to be a fractal sequence 1. If i+1=x_n, then there exists m<n such that i=x_m, 2. If h<i, ...

The Fransén-Robinson constant F is defined by F=int_0^infty(dx)/(Gamma(x))=2.8077702420... (OEIS A058655) where Gamma(x) is the gamma function. No closed-form expression in ...

A function f is Fréchet differentiable at a if lim_(x->a)(f(x)-f(a))/(x-a) exists. This is equivalent to the statement that phi has a removable discontinuity at a, where ...

A free Abelian group is a group G with a subset which generates the group G with the only relation being ab=ba. That is, it has no group torsion. All such groups are a direct ...