1
vote
1answer
162 views

Two equal cyclic subgroups of $S_n$ have conjugate generators

The statement is relatively simple but the proof is giving me some trouble. Any help will be very much appreciated: Let $a,b \in S_n$. Assuming $<a> = <b>$ show that $b$ is a conjugate of ...
4
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1answer
109 views

Orbits of $\mathbb{Z}/n\mathbb{Z}$ under automorphism subgroup action

Let $A\leq \rm{Aut}(\mathbb{Z}/n\mathbb{Z})$. I am interested in the orbits of $\mathbb{Z}/n\mathbb{Z}$ under the action of $A$, i.e. the sets $$\{\sigma i : \sigma \in A\},$$ where $i\in ...