Answer: Find Order of A, J, N and Subgroup of Each Possible Order

[vj9]

I have a problem a group consists of following element A,B,C,D,F,G,H,J,K,L,M,N.How can we find the order of elements A,J,N?

state the possible orders of the proper subgroups?

Here is the group table

... A B C D F G H J K L M N

A . C G J M B K A D N F H L
B . F H L K A M B N D C G J
C . J K D H G N C M L B A F
D. M L H C N F D A B K J G
F . L M N G H D F K J A B C
G . B A F N C H G L M J K D
H . A B C D F G H J K L M N
K . G C B L J A K F H D N M
L . N D K B M J L G C H F A
M . H F A J L B M C G N D K
N . K J G F D C N B A M L HFind a subgroup of each possible order

Can anyone please help me out with this problem?

 

[vj9]

Can we also find the order the group?

 

[Mark44]

I put the table in a code block to make to make it easier to read. This makes it easier to spot which element is the identity element.

I have a problem a group consists of following element A,B,C,D,F,G,H,J,K,L,M,N.


How can we find the order of elements A,J,N?

For this part, you want to find n such that Aⁿ = e, the identity element. Do the same for J and N.

state the possible orders of the proper subgroups?

Here is the group table

  . [B] A B C D F G H J K L M N[/B]
[B]A[/B] .  C G J M B K A D N F H L
[B]B[/B] .  F H L K A M B N D C G J
[B]C[/B] .  J K D H G N C M L B A F
[B]D[/B].   M L H C N F D A B K J G
[B]F[/B] .  L M N G H D F K J A B C
[B]G[/B] .  B A F N C H G L M J K D
[B]H[/B] .  A B C D F G H J K L M N
[B]K[/B] .  G C B L J A K F H D N M
[B]L[/B] .  N D K B M J L G C H F A
[B]M[/B] .  H F A J L B M C G N D K
[B]N[/B] .  K J G F D C N B A M L H

Find a subgroup of each possible order

Can anyone please help me out with this problem?

 

[vj9]

Thanks Mark,

I think the order for J and N is 2. I still have problems with A and what is the order of the whole table?

 

[Mark44]

I didn't notice it before, but the table is missing a row for J, so I don't know how you can tell that the order of J is 2. There are a bunch of elements whose order is 2. One of these is N.

I don't think it makes sense to talk about the order of the whole table, but it probably makes sense to talk about the order of the group. How is this term defined?

 

[vj9]

The elements of J are

D N M A K L J H F G C B

Yes it is the order of thr group. I have typed it wrong. In the question it is also asking for the rotations and reflections. The group table is for the symmetrices of a rectangular hexagon ( clockwise rotations of 60, 120, 180,,240 and 300, reflections in the mid points of opposite sides in the lines through opposite vertices but not in this order)

a) Find the identity,
b) inverse of each element,
c) order of A, J, N,
d) State with reasons, which of the elements are reflections and which are rotations.
e) state the possible orders of the proper group

This is my question.

 

[Mark44]

Here's the table with the missing row back in.

  . [B] A B C D F G H J K L M N[/B]
[B]A[/B] .  C G J M B K A D N F H L
[B]B[/B] .  F H L K A M B N D C G J
[B]C[/B] .  J K D H G N C M L B A F
[B]D[/B].   M L H C N F D A B K J G
[B]F[/B] .  L M N G H D F K J A B C
[B]G[/B] .  B A F N C H G L M J K D
[B]H[/B] .  A B C D F G H J K L M N
[b]J[/b] .  D N M A K L J H F G C B
[B]K[/B] .  G C B L J A K F H D N M
[B]L[/B] .  N D K B M J L G C H F A
[B]M[/B] .  H F A J L B M C G N D K
[B]N[/B] .  K J G F D C N B A M L H

Yes it is the order of thr group. I have typed it wrong. In the question it is also asking for the rotations and reflections. The group table is for the symmetrices of a rectangular hexagon ( clockwise rotations of 60, 120, 180,,240 and 300, reflections in the mid points of opposite sides in the lines through opposite vertices but not in this order)

a) Find the identity,
b) inverse of each element,
c) order of A, J, N,
d) State with reasons, which of the elements are reflections and which are rotations.
e) state the possible orders of the proper group

a) You already know the identity.
b) Go through the table and find the inverse of each element. E.g. A ? = E, where E represents the identity.
c) Do what I said in post 3.
d) All the reflections are order 2. If you reflect something twice, you get back to the same thing you started with. The rotations are of order 2, 3, 5, and 6. Note that a rotation of 180 degrees is the same as a reflection, so I don't think there's a way to tell the difference between a relection and a rotation by this amount. For the rotations, think about how many times you have to do a certain rotation to get back to where you started.
e) You're going to have subgroups of order 2, 3, 5, and 6. I don't remember the definition for the order of a group, but it might be the highest order of any element in the group. Check this, though - you want to be using the correct definition.

 

[vj9]

Thank You very much matt. Your answers are very helpful

 

[vj9]

Sorry typo. Thanks Mark

 

[vj9]

Hi Mark,

I am trying to figure out the relections and rotations. I am stuck on it. Any help please? I am unable to do it.

Thanks in advance.

 

[Mark44]

See what I said in part d in post 7.

 

[vj9]

For the above table, for the subgroup of order 3, find its left cosets and right cosets?

b)For the subgroup of index 3, find its left cosets and right cosets?

 

[Mark44]

For the above table, for the subgroup of order 3, find its left cosets and right cosets?

b)For the subgroup of index 3, find its left cosets and right cosets?

What is the subgroup of order 3? What are the definitions of left and right cosets? What's the difference between a subgroup of order 3 and a subgroup of index 3?

 

[vj9]

Hi Mark,

Thank for your help. I have sorted out the cosets. Can you help me on my statistics work. Here is the scenario. " I Just need to know which statistical method to use to carry out the data

The scenario is as follows

Since the 1960s there has been an ongoing campaign among Quebecois to separate from Canada and form an independent nation. Should Quebec separate, the ramifications for the rest of Canada, American States that border Quebec, the North American Free Trade Agreement and numerous multi-national corporations would be enormous. In the 1993 elections the pro-sovereigntist Bloc Quebecois won 54 of Quebec’s 75 seats in the House of Commons. In 1994 the separatist Parti Quebecois formed the provincial government in Quebec and promised to hold a referendum on separation. As with most political issues, polling plays an important role in trying to influence voters and to predict the outcome of the referendum vote. Shortly after the 1993 federal election, The Financial Magazine, in co-operation with several polling companies, conducted a survey of Quebecois.

A total of 641 adult Quebecois were interviewed. They were asked the following question. (Francophones were asked the question in French). The pollsters also recorded the language (English or French) in which the respondent answered.

If a referendum were held today on Quebec’s sovereignty with the following question, “Do you want Quebec to separate from Canada and become an independent country?” would you vote yes or no?

2 Yes
1 No

The responses were recorded and stored in columns 1 (planned referendum vote for Francophones) and 2(planned referendum vote for Anglophones)

Infer from the data:

a) If the referendum were held on the day of the survey, would Quebec vote to remain in Canada?

b) Estimate with 95% confidence the difference between French and English speaking Quebecers in their support for separation.