Noun | 1. | group - any number of entities (members) considered as a unit Synonyms: grouping |
2. | group - (chemistry) two or more atoms bound together as a single unit and forming part of a molecule Synonyms: chemical group, radical | |
3. | group - a set that is closed, associative, has an identity element and every element has an inverse Synonyms: mathematical group | |
Verb | 1. | group - arrange into a group or groups; "Can you group these shapes together?" |
2. | group - form a group or group together Synonyms: aggroup |
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. |