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Let R be a ring. If phi:R->S is a ring homomorphism, then Ker(phi) is an ideal of R, phi(R) is a subring of S, and R/Ker(phi)=phi(R).

A graph G is said to be flexible if the vertices of G can be moved continuously so that (1) the distances between adjacent vertices are unchanged, and (2) at least two ...

A 180 degrees rotation of a tangle. The word "flype" is derived from the old Scottish verb meaning "to turn or fold back." Tait (1898) used this word to indicate a different ...

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 ...

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.