Exercise 15.2.22. * Show that it is impossible to complete the following Cayley tables to make a group. O a b c d O a b c d a a a (a) b b (c) b С С d с d С d O a e d O a a a (b) b (d) b С С P II I 6 I I I ex P I I a b I I С I I I I e d I

Exercise 15.2.22. * Show that it is impossible to complete the following Cayley tables to make a group. O a b c d O a b c d a a a (a) b b (c) b С С d с d С d O a e d O a a a (b) b (d) b С С P II I 6 I I I ex P I I a b I I С I I I I e d I

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.1: Definition Of A Group

Problem 15E: In Exercises and, the given table defines an operation of multiplication on the set. In each case,...

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Question

Please do Part ABC and please show step by step and explain

Exercise 15.2.22. * Show that it is impossible to complete the following
Cayley tables to make a group.
a b c d
oa b c d
a
a a
(a) b
b
с
с
d
d
C
a
d
a b с
a
b
O
a
(b) b
С
d
b
b
I
с
(c) b
С
20
d
O
a
(d) b
С
d
OL
с
I
I
d
I

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