Abstract Algebra
4. Complete the classification of the groups of order 8, except
for isomorphism, to check that the only possibilities are
a) C8;
b) C4 × C2;
c) C2 × C2 × C2;
d) D4;
e) Q8 = {±1, ±i, ±j, ±k}, where i, j, k are imaginary units
satisfying i^2 = j^2 = k^2 = ijk = -1. Q8 is the group of
quaternion units.