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Show that {1, 2, 3} under multiplication modulo 4 is not a

Chapter 2, Problem 9E

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QUESTION:

Show that {1, 2, 3} under multiplication modulo 4 is not a group but that {1, 2, 3, 4} under multiplication modulo 5 is a group.

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QUESTION:

Show that {1, 2, 3} under multiplication modulo 4 is not a group but that {1, 2, 3, 4} under multiplication modulo 5 is a group.

ANSWER:

Step 1 of 3

To find:  under multiplication modulo  is not a group but that  under multiplication modulo  is a group.

Condition of group are:

(1) Associativity: The operation is associative, that is  for  on set.

(2) Identity: The element  in set such that  for all  on set.

(3) Inverses: For each element  in set, there is an element  in set such that .

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