# Abstract Algebra

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A couple of quick queries i have;

If i have a group, T defined as the set of all ordered triplets, of the form (A,B,C)

Am i correct in saying that the number of elements mod(T) in T is just 3! as there is 6 ways of ordering them??

If we have 2 permutations defined as G, and H; and were asked to use the fact that

G composed with H, (G o H)= H composed with G (H o G)

to show that (G o H)^2 = e

where e is the identity permutation.

Am i right in saying that ;

(G o H)^(-1) = (Ho G)

so

(GoH)=(HoG) => (GoH)*e=(GoH)^(-1) * e

(GoH)(GoH)=e

(G o H)^2 =e

I am hoping to obtain some clarification.

If i have a group, T defined as the set of all ordered triplets, of the form (A,B,C)

Am i correct in saying that the number of elements mod(T) in T is just 3! as there is 6 ways of ordering them??

If we have 2 permutations defined as G, and H; and were asked to use the fact that

G composed with H, (G o H)= H composed with G (H o G)

to show that (G o H)^2 = e

where e is the identity permutation.

Am i right in saying that ;

(G o H)^(-1) = (Ho G)

so

(GoH)=(HoG) => (GoH)*e=(GoH)^(-1) * e

(GoH)(GoH)=e

(G o H)^2 =e

I am hoping to obtain some clarification.

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#2

I don't really inderstand this question but go on examsolution website. It is very helpful. I use that all the time.

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#3

(Original post by

A couple of quick queries i have;

If i have a group, T defined as the set of all ordered triplets, of the form (A,B,C)

Am i correct in saying that the number of elements mod(T) in T is just 3! as there is 6 ways of ordering them??

If we have 2 permutations defined as G, and H; and were asked to use the fact that

G composed with H, (G o H)= H composed with G (H o G)

to show that (G o H)^2 = e

where e is the identity permutation.

Am i right in saying that ;

(G o H)^(-1) = (Ho G)

so

(GoH)=(HoG) => (GoH)*e=(GoH)^(-1) * e

(GoH)(GoH)=e

(G o H)^2 =e

I am hoping to obtain some clarification.

**Swaggoholic**)A couple of quick queries i have;

If i have a group, T defined as the set of all ordered triplets, of the form (A,B,C)

Am i correct in saying that the number of elements mod(T) in T is just 3! as there is 6 ways of ordering them??

If we have 2 permutations defined as G, and H; and were asked to use the fact that

G composed with H, (G o H)= H composed with G (H o G)

to show that (G o H)^2 = e

where e is the identity permutation.

Am i right in saying that ;

(G o H)^(-1) = (Ho G)

so

(GoH)=(HoG) => (GoH)*e=(GoH)^(-1) * e

(GoH)(GoH)=e

(G o H)^2 =e

I am hoping to obtain some clarification.

As for the second question, it looks to me as though you've assumed the result in order to prove the said result.

The step:

seems to me to be unconvincing unless I missed something.

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(Original post by

The set of all ordered triples of ABC does indeed have 6 elements.

As for the second question, it looks to me as though you've assumed the result in order to prove the said result.

The step:

seems to me to be unconvincing unless I missed something.

**joostan**)The set of all ordered triples of ABC does indeed have 6 elements.

As for the second question, it looks to me as though you've assumed the result in order to prove the said result.

The step:

seems to me to be unconvincing unless I missed something.

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#5

(Original post by

I agree, can you please give me some advice on answering this question.

**Swaggoholic**)I agree, can you please give me some advice on answering this question.

With any luck someone'll be along who'll sort you out

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(Original post by

Not without further clarification, sorry

With any luck someone'll be along who'll sort you out

**joostan**)Not without further clarification, sorry

With any luck someone'll be along who'll sort you out

thanks anyway bud

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#7

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(Original post by

The second part of your question isn't true. Take for example , and , where . Then . However, .

**0x2a**)The second part of your question isn't true. Take for example , and , where . Then . However, .

The question states that,

G o H = H o G

im asked to derive that;

(G o H) ^2 = e

where e is the identity

If the questin is wrong as you suggest, can you analogue a question that works, where you can show me the method of tackling this type of question?

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#9

(Original post by

The question states that,

G o H = H o G

im asked to derive that;

(G o H) ^2 = e

where e is the identity

If the questin is wrong as you suggest, can you analogue a question that works, where you can show me the method of tackling this type of question?

**Swaggoholic**)The question states that,

G o H = H o G

im asked to derive that;

(G o H) ^2 = e

where e is the identity

If the questin is wrong as you suggest, can you analogue a question that works, where you can show me the method of tackling this type of question?

If the exercise is from any respectable source then they would have told you that , or that if , where , it should have given you some restrictions on the types of permutations that are allowed, since if , and is not always the identity permutation.

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(Original post by

Where are you getting this question from? If it's from some book, could you also type in all the information that comes with it?

If the exercise is from any respectable source then they would have told you that , or that if , where , it should have given you some restrictions on the types of permutations that are allowed, since if , and is not always the identity permutation.

**0x2a**)Where are you getting this question from? If it's from some book, could you also type in all the information that comes with it?

If the exercise is from any respectable source then they would have told you that , or that if , where , it should have given you some restrictions on the types of permutations that are allowed, since if , and is not always the identity permutation.

G and H belong to S.

Does that help?

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#11

(Original post by

We define S as the set of all ordered triplets of the form (A,B,C).

G and H belong to S.

Does that help?

**Swaggoholic**)We define S as the set of all ordered triplets of the form (A,B,C).

G and H belong to S.

Does that help?

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#12

**Swaggoholic**)

We define S as the set of all ordered triplets of the form (A,B,C).

G and H belong to S.

Does that help?

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#13

**Swaggoholic**)

We define S as the set of all ordered triplets of the form (A,B,C).

G and H belong to S.

Does that help?

0

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