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. a) Find the conjugacy classes for Dg and write the class equation for Dg.

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. a) Find the conjugacy classes for Dg and write the class equation for Dg.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.8: Some Results On Finite Abelian Groups (optional)

Problem 14E: Suppose that the abelian group G can be written as the direct sum G=C22C3C3, where Cn is a cyclic...

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