Let G be a group with 4 (distinct) elements (e, a, b, c), where e is...

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Let G be a group with 4 (distinct) elements (e, a, b, c), where e is as usual the identity element. Write down the multiplication table for G if 1) the orders of a, b, c are 4, 2, 4, respectively, and 2) the order of every element is less than 4. These two criteria will give you two different groups, so you should give me two different multiplication tables. Make sure each entry in each table is justified. [10] Let G be a group with 4 (distinct) elements (e, a, b, c), where e is as usual the identity element. Write down the multiplication table for G if 1) the orders of a, b, c are 4, 2, 4, respectively, and 2) the order of every element is less than 4. These two criteria will give you two different groups, so you should give me two different multiplication tables. Make sure each entry in each table is justified. [10]

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1 For the first group since the orders of a and c are both 4 they must be generators of the group Th... View the full answer