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Next: Theorem 29.5: Up: Exercises Previous: Theorem 29.4:

Proof:

Thanks to (29.7), $ \phi_n$ maps $ Z_n(G)$ into $ Z_n(K)$ and $ B_n(G)$ into $ B_n(K)$. Thus the map induced on the quotient groups is a well defined group homomorphism.
nisha 2012-03-20