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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 GroupOrder[n].


See also

Abelian Group, Finite Group

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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 Order

Cite this as:

Weisstein, Eric W. "Group Order." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GroupOrder.html

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