croup

n 1: a disease of infants and young children; harsh coughing and

hoarseness and fever and difficult breathing [syn: {spasmodic

laryngitis}]

2: the part of a quadruped that corresponds to the human

buttocks [syn: {hindquarters}, {croupe}, {rump}]

group

A group G is a non-empty {set} upon which a {binary} operator

▫ is defined with the following properties for all a,b,c in G:

Closure: G is closed under ▫, a▫b in G

Associative: ▫ is associative on G, (a▫b)▫c ◦ a▫(b▫c)

Identity: There is an identity element e such that

a▫e ◦ e▫a ◦ a.

Inverse: Every element has a unique inverse a' such that

a ▫ a' ◦ a' ▫ a ◦ e. The inverse is usually

written with a superscript -1.

(1998-10-03)