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Explain why each of the following could not be the class equation of a group G. i) |G| = 3 + 3 + 3 ii) |G| = 2 + 3 + 3 +7 iii) |G| = 1 +3 + 6 + 8

Explain why each of the following could not be the class equation of a group G. i) |G| = 3 + 3 + 3 ii) |G| = 2 + 3 + 3 +7 iii) |G| = 1 +3 + 6 + 8

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The class equation for a group G can be written |G| = |Z(G)| + E|CI(a;), where the sum runs over representatives of the distinct non-central conjugacy classes. Recall that the conjugacy classes for S3 are {1}, {(123), (132)} and {(12), (13), (23)}. Therefore the class equation of S3 is given by | S3| =1+2 +3. b) Explain why each of the following could not be the class equation of a group G. i) |G| = 3 + 3 + 3 ii) |G| = 2 + 3 + 3 + 7 iii) |G| = 1 + 3 + 6 + 8
Transcribed Image Text:The class equation for a group G can be written |G| = |Z(G)| + E|CI(a;), where the sum runs over representatives of the distinct non-central conjugacy classes. Recall that the conjugacy classes for S3 are {1}, {(123), (132)} and {(12), (13), (23)}. Therefore the class equation of S3 is given by | S3| =1+2 +3. b) Explain why each of the following could not be the class equation of a group G. i) |G| = 3 + 3 + 3 ii) |G| = 2 + 3 + 3 + 7 iii) |G| = 1 + 3 + 6 + 8
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