Let p be a prime and let .
Prove that the only proper subgroups of are the finite cylic groups
For each positive integer k, define a function by .
Show that the kernel of the homomorphism is .
How should I proceed with this? Thank you!
Let p be a prime and let .
Prove that the only proper subgroups of are the finite cylic groups
For each positive integer k, define a function by .
Show that the kernel of the homomorphism is .
How should I proceed with this? Thank you!
i already answered this question at least twice! see here.
see that your function is a well-defined (additive) group homomorphism, although it's trivial! now: thus:For each positive integer k, define a function by .
Show that the kernel of the homomorphism is .
did i have to mention that the element of is the coset ? i think you know that ...