Here is a brief introduction.
Definition:
Let G be a nonempty set and * be its (binary) algebraic operation, if the following conditions are satisfied: i. The associative law holds, that is, any element A, B and C in G has (a * b) * c = a * (b * c); Two. There is an element E in G, which is called the left unit element of G, and it has e * a = a three for every element A in G. For every element A in G, there is an element A (- 1) in G, which is called the left inverse of A, so A (-1) * A = E; Then say that G did a set of algebraic operations *.
Nature:
Generally speaking, a group is a set g * that satisfies the following four conditions for an operation: (1) If a, b∈G, there is a unique and definite c∈G, so that a * b = c；;
(2) The associative law holds any a, b, c∈G, where (a * b) * c = a * (b * c);
(3) there is an identity e∈G, for any a∈G, a*e=e*a=a, so e is called an identity, also called unitary;
(4) If there is any a∈G in the inverse element and there is only b∈G, and a*b=b*a=e (unit element), then A and B are called inverse elements, called A (-1) = B. 。
The binary operation * on G is usually called "multiplication", and a*b is called the product of A and B, abbreviated as ab.
If the number of elements in a group G is finite, then G is called a finite group. Otherwise it is called infinite group. The number of elements of a finite group is called the order of a finite group.
Operators in group theory are similar to logical operators, but different from arithmetic operators, which can be understood by reading books.
I recommend you this classic textbook.
Zuo Xiaoling, Li Weijian and Liu Yongcai edited Discrete Mathematics.
Shanghai Science and Technology Literature Publishing House