Study group homomorphisms, which are structure-preserving maps between groups, and delve into isomorphisms, which are bijective homomorphisms that establish a one-to-one correspondence between groups.
Group Homomorphisms and Isomorphisms Homomorphism Definition A function f: G -> H between two groups that preserves the group operation: f(a*b) = f(a)*f(b) for all a, b in G. Kernel of a Homomorphism The set of elements in G that map to the identity element in H; the kernel is always a subgroup of G (in fact, a normal subgroup). Isomorphism A homomorphism that is also bijective (one-...…
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