Answers of 1st task a group

Answers of 1st task

A group is a finite or infinite set of elements together with a binary operation (called the group operation) that together satisfy the four fundamental properties of closure, associativity, the identity property, and the inverse property.

A group is a set G along with some operation · that takes in two elements and outputs another element of our group, such that we satisfy the following properties:

• Identity: there is a unique identity element e ∈ G such that for any other g ∈ G, we have e · g = g · e = g.

• Inverses: for any g ∈ G, there is a unique g −1 such that g · g −1 = g −1 g = e.

• Associativity: for any three a, b, c ∈ G, a · (b · c) = (a · b) · c.