Definition 2.10 A group (G, *, 1) consists of a set G with a binary operation * and an identity element 1 satisfying the following three axioms:
(Z, +, 0), (Zn, +, 0), (, ., 1)
The following definitions generalize Definitions 2.9.
Property 2.6 The order of an element x of a finite group G divides the number of elements in G..
Proof First observe that if H is a subgroup of G, then an equivalence ...