The tables shown below are examples of noncommutative, or nonabelian, groups. For each exercise, do the following.

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The tables shown below are examples of noncommutative, or nonabelian, groups. For each exercise, do the following.

(a) Show that the system under the given operation is a group. (It would be very time consuming to prove that the associative property holds, but give some examples to show that it appears to hold.)

(b) Determine a counterexample to show that the commutative property does not hold.


3 4 4 2 1 2 3 1 4 3 3 5 4 4 3 1 5 3 4 6. 3. 2. 2. 3. 6. 2. 2. 4,

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A Survey of Mathematics with Applications

ISBN: 978-0134112107

10th edition

Authors: Allen R. Angel, Christine D. Abbott, Dennis Runde

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