Jump to content

abstract algebra need help please!

Recommended Posts

i am not sure of this. havent done this for a while. but most likely you will have 22 rotational symmetries and 22 reflective symmetries. i am not going to list them all


but here are some rotational


(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22)


(1 3 5 7 9 11 13 15 17 19 21)(2 4 6 8 10 12 14 16 18 20)

Link to comment
Share on other sites

In what form are you used to seeing groups presented? From the question it just asks you what the symmetry group of a 22-gon is, which is either D(11) or D(22) depending on the standards in the course you're using. But how do *you* describe groups? There are many ways of doing it, which do you understand?


Bloodhounds description for instance amounts to labelling the corners, and the thing in bracket tells you what to do to each corner, the first is the symmetry sending the corner labelled 1 to that labelled 2, that labelled 2 to 3 and so on reading left to right.

This, sorry to say, bloodhound, is about the worst way of writing it since it contains so much redundant information: pick three adjacent corners, once you've said where to map them to the symmetry is fixed otherwise yo'ud have to break the cap. So there are 19 numbers in there that do nothing.


The best way, perhaps is in terms of generators and relations.

Link to comment
Share on other sites

Please bare with me I need help with a question : Why can't a set be defined


A set can be "defined", it just isn't defined how people first think it is defined.

It is not a collection of objects with some rule for belonging. How it should be done is messy and unilluminating at this stage in your development, since the *naive* definition is sufficient for many purposes.


As for "definition", that is philosophical, my preferred way is to think of the definition of an object as the set of rules that define its use.

Link to comment
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now
  • Create New...

Important Information

We have placed cookies on your device to help make this website better. You can adjust your cookie settings, otherwise we'll assume you're okay to continue.