# Homework Help: D4 question

1. Apr 18, 2010

### tyrannosaurus

1. The problem statement, all variables and given/known data
Prove that D4 (Dihedral group) cannot be expressed as an internal direct product of two proper subgroups.

2. Relevant equations

3. The attempt at a solution
I know that the only two possible subgroups would be the subgroups of order 4 and 2. I am thinking since D4 is not commutative I can get a contradicition this way, but I am not sure how to do it. Any help would be welcomed

2. Apr 18, 2010

### Dick

A direct sum can be nonabelian. But why not if the order of the factor groups are 2 and 4?

3. Apr 18, 2010

### Dickfore

The question states direct product, not sum.

4. Apr 18, 2010

### Dick

Is there a difference when you are talking about groups? There is only one binary operation. That's a silly comment.

5. Apr 18, 2010

### Dickfore

What's a direct product of two groups and what's a direct sum?

6. Apr 18, 2010

### Dick

The distinction is unimportant. You only choose to say one or the other depending on whether you are using the additive notation for the group operation or the multiplicative. The result is the same. Your comments are not very helpful.

7. Apr 18, 2010

### Dickfore

Neither are yours.

8. Apr 18, 2010

### Dick

Do you think there is a difference? What might it be?

Last edited: Apr 18, 2010