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Groups and FieldsChallengeDirect Products and Finite Abelian Groups

Direct Products and Finite Abelian Groups · Challenge problem

G=Z4×Z6G=\mathbb Z_4\times\mathbb Z_6, order 2424. Let H={(a,b):a and b have the same parity}H=\{(a,b): a\text{ and }b\text{ have the same parity}\}. What is [G:H][G:H]?