The identity element of a group is unique.
Finite groups can be expressed with a Cayley table
The order of a group is the number of elements in it.
A cyclic group is a group that has an element such that every element in the group can be “generated” by applying the binary operator repeatedly to that element, or to it’s inverse.
If the group is cyclic, then the group is abelian.
Let A be a group with binary operator □ and B be a group with binary operator △.
Group A is homomorphic to group B if there exists a transformation φ where φ maps elements from A to B, and for all a, a’ in A, φ(a □ a’) = φ(a) △ φ(a’).
Elliptic curve points under addition modulo p are a cyclic finite group and integers under addition are homomorphic to this group.