(adsbygoogle = window.adsbygoogle || []).push({}); Question

Let[itex]S_n[/itex]be the symmetric group on[itex]n[/itex]letters.

(i)Show that if[itex]\sigma = (x_1,\dots,x_k)[/itex]is a cycle and[itex]\phi \in S_n[/itex]then

[tex]\phi\sigma\phi^{-1} = (\phi(x_1),\dots,\phi(x_k))[/tex]

(ii)Show that the congujacy class of a permutation [itex]\sigma \in S_n[/itex] consists of all permutations in [itex]S_n[/itex] of the same cycle type as [itex]\sigma[/itex]

(iii)In the case of [itex]S_5[/itex], give the numbers of permutations of each cycle type

(iv)Find all normal subgroups of [itex]S_5[/itex]

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Cycles and Permutations

**Physics Forums | Science Articles, Homework Help, Discussion**