Mathematics desk | ||
---|---|---|
< December 10 | << Nov | December | Jan >> | Current desk > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is a transcluded archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
Let H be a group of order n, K = Aut(H), and G = H x K where x is the semidirect product with respect to the identity homomorphism . Let G act on the set X of left cosets of K in G by left multiplication, inducing a permutation representation π from G into Sn. Why do we have that
I've shown that the left side is a subset of the right, but I can't get the reverse inclusion. The textbook hints that
could be helpful for proving
but I can't see why. Thanks in advance for any help. — Anonymous Dissident Talk 13:54, 11 December 2012 (UTC)
I'm trying to figure out the following question (The answer may be at Fibonacci number#Prime divisors of Fibonacci numbers, but I'm not seeing it.) Is the following true: For all prime p there exists k such that p|Fk . If so, is there a way to calculate a k so it is true? If so, is there a way to calculate the smallest k so that it is true?
How did Euler prove the sum of the reciprocals of the primes diverges? I know he created the Riemann zeta function for it but how did he do this? — Preceding unsigned comment added by 86.185.99.78 (talk) 21:18, 11 December 2012 (UTC) — Preceding unsigned comment added by 86.185.99.78 ( talk)
These proofs are interesting but none address how he developed the Riemann zeta function to help his argument. Some of them use the sum of 1/n but none use 1/(n^s) — Preceding unsigned comment added by 86.185.99.78 ( talk) 23:19, 11 December 2012 (UTC)
Mathematics desk | ||
---|---|---|
< December 10 | << Nov | December | Jan >> | Current desk > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is a transcluded archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
Let H be a group of order n, K = Aut(H), and G = H x K where x is the semidirect product with respect to the identity homomorphism . Let G act on the set X of left cosets of K in G by left multiplication, inducing a permutation representation π from G into Sn. Why do we have that
I've shown that the left side is a subset of the right, but I can't get the reverse inclusion. The textbook hints that
could be helpful for proving
but I can't see why. Thanks in advance for any help. — Anonymous Dissident Talk 13:54, 11 December 2012 (UTC)
I'm trying to figure out the following question (The answer may be at Fibonacci number#Prime divisors of Fibonacci numbers, but I'm not seeing it.) Is the following true: For all prime p there exists k such that p|Fk . If so, is there a way to calculate a k so it is true? If so, is there a way to calculate the smallest k so that it is true?
How did Euler prove the sum of the reciprocals of the primes diverges? I know he created the Riemann zeta function for it but how did he do this? — Preceding unsigned comment added by 86.185.99.78 (talk) 21:18, 11 December 2012 (UTC) — Preceding unsigned comment added by 86.185.99.78 ( talk)
These proofs are interesting but none address how he developed the Riemann zeta function to help his argument. Some of them use the sum of 1/n but none use 1/(n^s) — Preceding unsigned comment added by 86.185.99.78 ( talk) 23:19, 11 December 2012 (UTC)