Thread: D8 subgroups

Easy question. How do I find the subgroups of ?

See Deveno's posts in answer to my post "Normal Subgroups in D4 "

Peter

Originally Posted by Bernhard

See Deveno's posts in answer to my post "Normal Subgroups in D4 "

Peter

So the Centralizer of each element is a subgroup then?

And normal subgroups are in the center?

What about cyclic?

Sorry.

I was too quick in referrring you to my post - I was looking for normal subgroups only.

Peter

Originally Posted by Bernhard

Sorry.

I was too quick in referrring you to my post - I was looking for normal subgroups only.

Peter

It didn't matter I learned something from it.

So the cyclic subgroups are , correct?

Yes, but I think there may be others of order 2 such as <s> = {s, e} and <sr> = {sr, e}

Do you agree?

Peter

Originally Posted by Bernhard

Yes, but I think there may be others of order 2 such as <s> = {s, e} and <sr> = {sr, e}

Do you agree?

Peter

How were you able to identify those at cyclic groups?

Just by checking the subgroups generated by the elements concerned - no smart method - just working through the elements of the group checking the subgroups generated by each element. If the group concerned was very much bigger you would have to be more analytic I guess.

Another possibility is < > = {e, } and of course there is {e}.

Peter