thanks i understand it now! :)
also another question
Let H be any subgroup of G other than G itself. explain why H is cyclic?
since G is prime then |H| is 1 or 7. then H must equal G and it would be cyclic but the question says any other subgroup other than G so H must be {e}? is this cyclic...
Let G be the group of symmetries (including flips) of the regular heptagon (7-gon).
As usual, we regard the elements of G as permutations of the set of vertex labels; thus, G ≤ S7.
(a) Let σ denote the rotation of the 7-gon that takes the vertex 1 to the vertex 2. Write down the cyclic...
I'm trying to figure out how to prove this, but I'm unsure how to approach it.
Let G and H be groups, let ϕ: G → H be an isomorphism, and let ψ be the inverse function of ϕ. Prove that ψ is an isomorphism from H to G.
any help? thanks