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.

• Korselt's Criterion
• Kovalevskaya Exponent
• Kozyrev-Grinberg Theory
• k-Partite Graph
• Kramers Rate
• Krawtchouk Polynomial
• Kreisel Conjecture
• Kronecker Decomposition Theorem
• Kronecker Delta
• Kronecker Product
• Kronecker's Polynomial Theorem
• Kronecker Symbol
• Krull Dimension
• Kruskal's Algorithm
• Kruskal's Tree Theorem
• KS Entropy
• k-Statistic
• k-Subset
• k-Theory
• k-Tuple Conjecture
• Kuen Surface
• Kuhn-Tucker Theorem
• Kuiper Statistic
• Kulikowski's Theorem
• Kummer Group