Homework Statement
If p and q are prime numbers, p>q>2 , and 1+k*p divides q^n for some positive integer n. What can i expect of the values of k ? Does it works just for k=0 ?
Homework Equations
q^n = 1 (mod p)
The Attempt at a Solution
I know that k=0 works , and k=odd don't...
I think i got it, if i take S_3 then for all a , b \in S_3 we have
(a.b)^0=e=e.e=a^0.b^0 and
(a.b)^1=a^1.b^1
Hence (a.b)^i=a^i.b^i for two consecutive integers but S_3 is not abelian.
Homework Statement
If G is a group in which (a.b)^i=a^i.b^i for three consecutive integers i for all a,b \in G , show that G is abelian.
Show that the conclusion does not follow if we assume the relation (a.b)^i=a^i.b^i for just two consecutive integers.
Homework Equations
The...