Question

State the Lagrange Theorem, and find the order of all possible subgroups of a group of order 5. The same question of a group of order 6.

Answer 1

Lagrange Theorem

Explanation:

The Lagrange Theorem:

Let G be a finite group and T be a subgroup of G. Then the order of T divides the Order of group G.

This can be written as:

If
`T \subset G`, then,
`o(T)|o(G)`.

Possible Subgroups

Now, we are given a group with order 5. We have to find all possible subgroups.

So, the possible subgroup are: groups with order 1, group with order 5

We are given a group with order 6.

Possible subgroups are: group of order 1, group of order 2, group of order 3 and group of order 4.