abstract algebra need help please!

[cuti3panda]

Bottle caps that are pried off typically have 22 ridges around the rim. Find the symmetry group of such a cap.

 

Please help me this problem, thanks a lot!

[bloodhound]

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)

[matt grime]

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.

[cuti3panda]

Matt Grime, would you plz give me more detail about the problem above! it's due on thursday, help me plz....thanks a lot

[matt grime]

Any basic group theory book will explain what dihedral groups are.

[cuti3panda]

thanks again, matt grime!

[Guest John Doe]

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

[Guest John Doe]

What does mathematics has to say about the term "definition".These are some question ask by my professer

[bloodhound]

This' date=' sorry to say, bloodhound, is about the worst way of writing it since it contains so much redundant information: .[/quote']

Hehe , I DID say i havent done this for a while.

[matt grime]

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.