Math Is Fun Forum

laipou

Member

Registered: 2009-09-19

Posts: 24

Some problems in group theory

1.What is the commutator group of A4?
   Is there any simple idea to solve this problem?
2.Determine all conjugacy classes of 4*4 matrices A over R such that A^3 = A
   I have seen the word "conjugacy classes" in group actions.
   But I don't understand what it means here.
3.Show that there exists a subgroup H of a group G such that G is finitely generated but H is not finitely generated.
   I know G must be non-abelian.but I can't find one.

Thanks!

mynilam

Member

Registered: 2009-11-08

Posts: 1

Re: Some problems in group theory

The following table shows the distribution of monthly groceries expenditure (in thousands RM) of 35 housewives.

Amount of money spent
   
0.5-1.0
   
1.5-2.0
   
2.5-3.0
   
3.5-4.0
   
4.5-5.0

Frequency
   
3
   
12
   
9
   
7
   
4

Based on the above data, calculate the mean, median and mode of monthly groceries expenditure made by the housewives.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Some problems in group theory

Hi mynilam;

This topic doesn't belong here. You should have started a new topic I think.

I am uncomfortable with the question and here is why.

The mode is the most frequent observation in the data. But it is for discrete data. Meaning:

{1,1,2,2,2,3,4,5,5,5,5,5,6,6,7,8,9,9,9,9}

Here the mode would be 5. Your data is continuous. From what I understand the mode now has no meaning. You can provide your data as a histogram.

Last edited by bobbym (2009-11-09 09:27:23)

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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.

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Some problems in group theory

1.What is the commutator group of A4?
   Is there any simple idea to solve this problem?

What do you know about the commutator?  Does the property:

[G,G] is the smallest group such that G/[G,G] is abelian.

Sound familiar?

Determine all conjugacy classes of 4*4 matrices A over R such that A^3 = A
   I have seen the word "conjugacy classes" in group actions.
   But I don't understand what it means here.

A is conjugate to B if and only if there exists some matrix J such that

If you don't know the Rational canonical form, you won't be able to solve this problem.

Show that there exists a subgroup H of a group G such that G is finitely generated but H is not finitely generated.

Think free groups.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."