In Exercises determine whether the given map ϕ is a homomorphism. [Hint: The straightforward way to proceed is to check whether ϕ (ab) = ϕ(a) ϕ(b) for all a and b in the domain of ϕ. However, if we should happen to notice that ϕ-1 [{e'}] is not a subgroup whose left and right cosets coincide, or that ϕ does not satisfy the properties given in Exercise 44 or 45 for finite groups, then we can say at once that ϕ is not a homomorphism.
Let ϕ : ℤ → ℝ under addition be given by ϕ(n) = n.
We need at least 10 more requests to produce the solution.
0 / 10 have requested this problem solution
The more requests, the faster the answer.