Question

Define a group with a suitable example. When does it become abelian?

A) When the order is odd
B) When the order is even
C) When the group operation is commutative
D) When the group has no identity element

Answer 1

C) When the group operation is commutative. A group in mathematics consists of a set of elements with an operation and satisfies certain properties. An abelian group is a group in which the operation is commutative.

Step-by-step explanation:

A group in mathematics is a set of elements with an operation that satisfies certain properties. Specifically, a group consists of a set of elements, an operation (such as addition or multiplication), and four properties: closure, associativity, identity element, and invertibility.

For example, the set of integers under addition form a group because the operation of addition is closed, associative, there is an identity element (zero), and each element has an inverse (the negative).

An abelian group, also known as a commutative group, is a group in which the operation is commutative. This means that for any two elements a and b in the group, a*b = b*a.

So, the correct answer to the question is C) When the group operation is commutative.