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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 ...

The Fermat axis is the central line connecting the first and second Fermat points. It has line function l=a(b^2-c^2)(a^2-b^2-bc-c^2)(a^2-b^2+bc-c^2), corresponding to ...

The Feuerbach triangle is the triangle formed by the three points of tangency of the nine-point circle with the excircles (Kimberling 1998, p. 158). (The fact that the ...

A fibered category F over a topological space X consists of 1. a category F(U) for each open subset U subset= X, 2. a functor i^*:F(U)->F(V) for each inclusion i:V↪U, and 3. ...

Let F and G be fibered categories over a topological space X. A morphism phi:F->G of fibered categories consists of: 1. a functor phi(U):F->G(U) for each open subset U ...

A field automorphism of a field F is a bijective map sigma:F->F that preserves all of F's algebraic properties, more precisely, it is an isomorphism. For example, complex ...

For a field K with multiplicative identity 1, consider the numbers 2=1+1, 3=1+1+1, 4=1+1+1+1, etc. Either these numbers are all different, in which case we say that K has ...

The q-series identity product_(n=1)^(infty)((1-q^(2n))(1-q^(3n))(1-q^(8n))(1-q^(12n)))/((1-q^n)(1-q^(24n))) = ...

An extension field F subset= K is called finite if the dimension of K as a vector space over F (the so-called degree of K over F) is finite. A finite field extension is ...

A graph with a finite number of nodes and edges. If it has n nodes and has no multiple edges or graph loops (i.e., it is simple), it is a subgraph of the complete graph K_n. ...