If ahas nite order, we de ne the order of ato be the smallest positive integer nsuch that an= e. For example, 1 2Z has in nite order (when Z is considered a group under addition), but 1 2Z 5 has order 5 (when Z 5 is considered a group under the modi ed addition). (**) Let Gbe a group and let a2Ghave order n. Then it is not hard to show that a 1 ...
Mar 01, 2018 · Let L (X) be a 2-NLP over F q n and γ be an element of order s in the multiplicative group F q ⁎. Then the functional graph G L + γ X has one cycle of length 1, z L − 1 s cycles of length s and q n − z L p s cycles of length ps, where z L = # Z L is the number of roots of L in F q n.