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If F is a group, then the extensions G of F of order o with G/phi(G)=F, where phi(G) is the Frattini subgroup, are called Frattini extensions.

A group given by G/phi(G), where phi(G) is the Frattini subgroup of a given group G.

The intersection phi(G) of all maximal subgroups of a given group G.

A semigroup with a noncommutative product in which no product can ever be expressed more simply in terms of other elements.

A group acts freely if there are no group fixed points. A point which is fixed by every group element would not be free to move.

The French metro metric is an example for disproving apparently intuitive but false properties of metric spaces. The metric consists of a distance function on the plane such ...

A friend of a number n is another number m such that (m,n) is a friendly pair.

Almost all natural numbers are very, very, very large (Steinbach 1990, p. 111).

Let F be a field of field characteristic p. Then the Frobenius automorphism on F is the map phi:F->F which maps alpha to alpha^p for each element alpha of F.

If f^'(x) is continuous and the integral converges, int_0^infty(f(ax)-f(bx))/xdx=[f(0)-f(infty)]ln(b/a).