You are Here: Home

# Subgroup Group Theory

Maths and statistics discussion, revision, exam and homework help.

This thread is sponsored by:
Announcements Posted on
Find out how cards are replacing warnings on TSR...read more 03-12-2013
Important: please read these guidelines before posting about practical exams on The Student Room 26-11-2013
1. Subgroup Group Theory

I need to show that the question number 3 is a subgroup.

I have to go all the axioms of the subgroup.

Can you please help?
2. Re: Subgroup Group Theory
For the closure under addition

if x,y are in H where tanx, tay are in Q then I have to show that

x+y=xy ?
3. Re: Subgroup Group Theory
(Original post by maths27)
For the closure under addition

if x,y are in H where tanx, tay are in Q then I have to show that

x+y=xy ?
Dude this makes no sense. To show closure under addition, you want to show that x+y is in H.

The fastest way to show something is a subgroup is often the two step test:

check H is non-empty. (if H is empty it ain't a subgroup)
check that if x and y are in H, then x-y is in H

you should be able to show that these two conditions are equivalent to H being a subgroup (i.e. closure under addition and inverses). It's not much different but a tad neater/faster.
Last edited by Hathlan; 01-03-2012 at 11:32.
4. Re: Subgroup Group Theory
x+y in H but tanx and tany but be also in Q, How are we going to show that/
5. Re: Subgroup Group Theory
(Original post by maths27)
x+y in H but tanx and tany but be also in Q, How are we going to show that/
No offense, but it would help if you could write this in intelligible English.
6. Re: Subgroup Group Theory
For closure:

x,y ∈H, then tanx ∈Q and tany ∈Q.

Now we have to check that x+y ∈H, which means we have check whether tan(x+y)∈Q

from the formula:

tan(x+y)= (tanx+tany)/(1-tanx*tany)

so (rational + rational)/ (1-rational*rational)= 2rational / (1-rational^2) which gives rational ?
7. Re: Subgroup Group Theory
(Original post by maths27)
For closure:

x,y ∈H, then tanx ∈Q and tany ∈Q.

Now we have to check that x+y ∈H, which means we have check whether tan(x+y)∈Q

from the formula:

tan(x+y)= (tanx+tany)/(1-tanx*tany)

so (rational + rational)/ (1-rational*rational)= 2rational / (1-rational^2) which gives rational ?
Usually, but not always.

Hint: division by 0...
8. Re: Subgroup Group Theory
if we say that 1-rational^2 must not be equal to 0.

then we find that rational is not equal to 1.

just this?
9. Re: Subgroup Group Theory
Two things: The denominator is (1 - AB) where A = tan x, B = tan y, so you should only think of (1-rational^2) as shorthand; it might be that A = 1/2 and B = 2, say.

In any event, if you choose x, y s.t. AB = 1, then tan(x+y) isnt in Q. It's not hard to see that this can happen.
10. Re: Subgroup Group Theory
yes. when tanx*tany then=1 the tan(x+y) is not in Q. So the closure does not hold?
11. Re: Subgroup Group Theory
(Original post by maths27)
yes. when tanx*tany then=1 the tan(x+y) is not in Q. So the closure does not hold?
Correct. In particular, is in H, but what happens when we add ?
12. Re: Subgroup Group Theory
tan(pi/2) goes to infinity. So it is not a subgroup of real numbers with addition?
13. Re: Subgroup Group Theory
Our lecturer told as that it is a subgroup of this group.......
14. Re: Subgroup Group Theory
(Original post by maths27)
Our lecturer told as that it is a subgroup of this group.......
Your lecturer's wrong. Certainly since . If were a subgroup of then we'd have by closure under the group operation; but this is and we certainly don't have !
15. Re: Subgroup Group Theory
(Original post by nuodai)
Your lecturer's wrong. Certainly since . If were a subgroup of then we'd have by closure under the group operation; but this is and we certainly don't have !
I have to say, the "hint" leads you towards a "yes it does form a subgroup" answer, so I'm not totally surprised to see the lecturer saying this.

But as you say, he's wrong.

Submit reply

## Step 2: Register

Thanks for posting! You just need to create an account in order to submit the post
1. this can't be left blank
that username has been taken, please choose another Forgotten your password?

this is what you'll be called on TSR

2. this can't be left blank
this email is already registered. Forgotten your password?

never shared and never spammed

3. this can't be left blank

6 characters or longer with both numbers and letters is safer

4. this can't be left empty
your full birthday is required
1. By completing the slider below you agree to The Student Room's terms & conditions and site rules

2. Slide the button to the right to create your account

Slide to join now Processing…

You don't slide that way? No problem.

Last updated: March 1, 2012
Study resources
Article updates
Moderators

We have a brilliant team of more than 60 volunteers looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is moderated by:
Reputation gems:
You get these gems as you gain rep from other members for making good contributions and giving helpful advice.
Post rating score:
These scores show if a post has been positively or negatively rated by our members.