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A solvable group is a group having a normal series such that each normal factor is Abelian. The special case of a solvable finite group is a group whose composition indices ...

If, for n>=0, beta_n=sum_(r=0)^n(alpha_r)/((q;q)_(n-r)(aq;q)_(n+r)), (1) then beta_n^'=sum_(r=0)^n(alpha_r^')/((q;q)_(n-r)(aq;q)_(n+r)), (2) where alpha_r^' = ...

A bar (also called an overbar) is a horizontal line written above a mathematical symbol to give it some special meaning. If the bar is placed over a single symbol, as in x^_ ...

The term Bol loop refers to either of two classes of algebraic loops satisfying the so-called Bol identities. In particular, a left Bol loop is an algebraic loop L which, for ...

A cyclic polygon is a polygon with vertices upon which a circle can be circumscribed. Since every triangle has a circumcircle, every triangle is cyclic. It is conjectured ...

The decimal period of a repeating decimal is the number of digits that repeat. For example, 1/3=0.3^_ has decimal period one, 1/11=0.09^_ has decimal period two, and ...

There are two important theorems known as Herbrand's theorem. The first arises in ring theory. Let an ideal class be in A if it contains an ideal whose lth power is ...

A homogeneous linear ordinary differential equation with constant coefficients is an ordinary differential equation in which coefficients are constants (i.e., not functions), ...

An inhomogeneous linear ordinary differential equation with constant coefficients is an ordinary differential equation in which coefficients are constants (i.e., not ...

A Kähler metric is a Riemannian metric g on a complex manifold which gives M a Kähler structure, i.e., it is a Kähler manifold with a Kähler form. However, the term "Kähler ...