Paper 3, Section I, D

Algebra and Geometry | Part IA, 2007

What does it mean to say that groups GG and HH are isomorphic?

Prove that no two of C8,C4×C2C_{8}, C_{4} \times C_{2} and C2×C2×C2C_{2} \times C_{2} \times C_{2} are isomorphic. [Here CnC_{n} denotes the cyclic group of order nn.]

Give, with justification, a group of order 8 that is not isomorphic to any of those three groups.

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