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Index is multiplicative

49 bytes added, 23:32, 15 November 2015
Size of the inverse images
==== Size of the inverse images ====
'''To prove'''': Consider the map <math>\varphi: G/K \to G/H</math>. Choose <math>g \in G</math> and consider the left coset <math>gH</math>. Then, the subset of <math>G/K</math> comprising left cosets contained in <math>gH</math> (i.e., left cosets that map to <math>gH</math> under <math>\varphi</math> ) can be put in bijection with <math>H/K</math>.
'''Proof''': We explicitly construct such a bijection <math>\psi</math> based on the choice of <math>g</math>, defined as:
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