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Results tagged with finite-groups
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user 246663
Questions on group theory which concern finite groups.
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Are there always more conjugacy classes in the kernel of a morphism to $Z_2$ than not?
Let $G$ be a finite group and let $\phi:G\to Z_2$ be a homomorphism to the group with two elements. Is it always the case that there are more conjugacy classes in the kernel of $\phi$ than conjugacy c …
- 44.4k
13
votes
Are there always more conjugacy classes in the kernel of a morphism to $Z_2$ than not?
I have a solution to the case of a general cyclic quotient which follows @diracdeltafunk's answer on MSE.
If $A=Z_n$ is cyclic then we can treat $\phi:G\to Z_n\hookrightarrow\mathbb{C}$ as a one dime …
- 513