Order (Group)
The number of elements in a Group 
, denoted 
. The order of an element 
of a finite group is thesmallest Power of 
such that 
, where 
is the Identity Element. In general, finding the order ofthe element of a group is at least as hard as factoring (Meijer 1996). However, the problem becomes significantlyeasier if and the factorization of are known. Under these circumstances, efficientAlgorithms are known (Cohen 1993).
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.
- Alternate Algebra
- Alternating Algebra
- Alternating Group
- Alternating Knot
- Alternating Knot Diagram
- Alternating Link
- Alternating Permutation
- Alternating Series
- Alternating Series Test
- Alternative Link
- Altitude
- Alysoid
- Ambient Isotopy
- Ambiguous
- Ambrose-Kakutani Theorem
- Amenable Number
- Amicable Numbers
- Amicable Pair
- Amicable Quadruple
- Amicable Triple
- Amortization
- Ampersand Curve
- Amphichiral
- Amphichiral Knot
- Amplitude