- #1

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{ p,p+q,pq, p^q , q^p}.

Determine which of the foll are the 3 elements in H

a. pq, p^q, q^p

b. P+q, pq,p^q

c. p, p+q, pq

d. p, p^q, q^p

e. p, pq, p^q

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- Thread starter mansi
- Start date

- #1

- 61

- 0

{ p,p+q,pq, p^q , q^p}.

Determine which of the foll are the 3 elements in H

a. pq, p^q, q^p

b. P+q, pq,p^q

c. p, p+q, pq

d. p, p^q, q^p

e. p, pq, p^q

- #2

matt grime

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- #3

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thanks sir, but could you please elaborate further.

i don't seem to get the idea...

i don't seem to get the idea...

- #4

matt grime

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A group for instance cannot contain p and q if they are coprime and not be all of Z since there are a and b in Z such that ap+bq=1, hence the group contains all elements of Z.

And I tihnk you ought to ponder that for a while, cos I really have given you more information than I want to.

- #5

matt grime

Science Advisor

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p=2 q=3

If 2 and 3 are in the group, then so is -2 (inverses) and hence, so is 3-2=1 (composition)

If 1 is in there so is 1+1+1+..+1= n (composition) and n was arbitrary, also -n is in there (inverses again)

- #6

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well...thanks a lot, sir!! i figured it out...

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