Order of a group
This article is about a basic definition in group theory. The article text may, however, contain advanced material.
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This article defines an arithmetic function on groups
View other such arithmetic functions
QUICK PHRASES: size of a group, cardinality of a group, size of the underlying set, number of elements
The order of a group is the cardinality of its underlying set.
Definition with symbols
The order of a group is the cardinality of as a set. it is denoted as .
The converse is not always true, that is, there may exist numbers dividing the order of the group with no subgroups of those orders.
The order of any quotient of a group also divides the order of the group.
The GAP command to compute the order of a group is:
group</math> may either be an on-the-spot definition of a group or a name for something defined earlier.