Prove that any two groups with one element are isomorphic.
Prove that any two groups with two elements are isomorphic.
Prove that any two groups with three elements are
isomorphic.
(i) There are two non-isomorphic groups of order 4: C4 and
C2xC2. Let C3 be a cyclic group of order 3. For each group G of
order 4, determine all possible homomorphisms f an element of
Hom(C3, Aut(G)).
(ii) For C3 and each G of order 4 as above, determine all
possible homomorphisms phi an element of Hom(G, Aut(C3)).