Group Order
The number of elements in a group 👁 G
, denoted 👁 |G|
. If the order of a group is a
finite number, the group is said to be a finite group.
The order of an element 👁 g
of a finite group 👁 G
is the smallest power of 👁 n
such that 👁 g^n=I
, where 👁 I
is the identity element.
In general, finding the order of the element of a group is at least as hard as factoring
(Meijer 1996). However, the problem becomes significantly easier if 👁 |G|
and the factorization of 👁 |G|
are known. Under these circumstances, efficient algorithms
are known (Cohen 1993).
The group order can be computed in the Wolfram Language using the function [n].
See also
Abelian Group, Finite GroupExplore with Wolfram|Alpha
More things to try:
References
Cohen, H. A Course in Computational Algebraic Number Theory. New York: Springer-Verlag, 1993.Meijer, A. R. "Groups, Factoring, and Cryptography." Math. Mag. 69, 103-109, 1996.Referenced on Wolfram|Alpha
Group OrderCite this as:
Weisstein, Eric W. "Group Order." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/GroupOrder.html