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Consider the group (Z13 − {0}, ·13). (Use MS Excel to construct the multiplication chart.) Let...

Consider the group (Z13 − {0}, ·13). (Use MS Excel to construct the multiplication chart.) Let H denote the subgroup generated by [4] and letK be the subgroup generated by [5].

a.) Calculate the groups HK and H ∩ K.

b.) Calculate the groups HK/K and H/(H ∩ K) and show that they are isomorphic.

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