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Suppose the table below is a group table. Fill in the

Chapter 2, Problem 33E

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QUESTION:

Suppose the table below is a group table. Fill in the blank entries.

Questions & Answers

QUESTION:

Suppose the table below is a group table. Fill in the blank entries.

ANSWER:

Step 1 of 5

Consider the following properties of group;

   * It has a unique identity element, .

   * For each element, the inverse is unique.

In order to be a group, no entry in the Cayley table should repeat in its corresponding row and column.

This property can be used to complete the table.

Apply the property of unique identity element to complete the first row and first column,

*

e

a

b

c

d

e

e

a

b

c

d

a

a

b

-

-

e

b

b

c

d

e

-

c

c

d

-

a

b

d

d

-

-

-

-

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