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#1 2011-10-28 23:29:34

sheldon69
Member
Registered: 2011-10-28
Posts: 2

conjugacy classes

Hi, another question from my textbook I can't seem to get.

Q: Let G be the group of matrices of the form

where
and
. Determine the conjugacy classes in G, and sketch them in the (x,y)-plane.

Thanks for any help. smile

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#2 2012-10-14 07:47:46

scientia
Member
Registered: 2009-11-13
Posts: 224

Re: conjugacy classes

The inverse of the matrix
is
. Let's calculate the conjugate of the matrix
by the matrix
:

Hence the conjugacy class containing

is
.

Last edited by scientia (2012-10-14 21:10:03)

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#3 2012-10-14 08:34:07

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,030

Re: conjugacy classes

scientia wrote:

This step doesn't look right.


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#4 2012-10-14 11:01:56

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 108,525

Re: conjugacy classes

Hi all;

anonimnystefy wrote:

This step doesn't look right.

You are correct.

Hi scientia;


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#5 2012-10-14 21:10:53

scientia
Member
Registered: 2009-11-13
Posts: 224

Re: conjugacy classes

Thanks for pointing out. smile

I've corrected the error in my post.

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