Determine whether the given system forms (a) a group and (b) an Abelian group. Natural numbers under multiplication
A) Abelian group
B) a group but not an Abelian group
C) Abelian group but not a group
D) not a group

Question

Quizplus · Accepted Answer

The natural numbers under multiplication do not form a group because there is no identity element (1 is not a natural number in some definitions) and not every element has an inverse within the natural numbers.

Determine Whether the Given System Forms (A) a Group and (B)