How many groups of order 7 are there? There is, up to isomorphism, a unique group of order 7, namely cyclic group:Z7.
Which is an example of a group? Example 1: Show that the set of all integers … -4, -3, -2, -1, 0, 1, 2, 3, 4, … is an infinite Abelian group with respect to the operation of addition of integers.
What is the smallest group? The trivial group.
Every group has an identity element, so the smallest possible order of a group is 1. And taken by itself, a group with only the identity element as an element is a group. It’s called the trivial group.
What are the groups of order 5?
|4||5||Elementary. Product. (Klein four-group. The smallest non-cyclic group.)|
|5||6||Simple. Cyclic. Elementary.|
|7||9||Simple. Cyclic. Elementary.|