Let be a prime. Show that where is any transposition and any -cycle.
Let and . (We have for some .) By a previous exercise, for some . Because has prime order, . Relabeling the elements , by the previous exercise we have .
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Let be a prime. Show that where is any transposition and any -cycle.
Let and . (We have for some .) By a previous exercise, for some . Because has prime order, . Relabeling the elements , by the previous exercise we have .
On these pages you will find a slowly growing (and poorly organized) list of proofs and examples in abstract algebra.
No doubt these pages are riddled with typos and errors in logic, and in many cases alternate strategies abound. When you find an error, or if anything is unclear, let me know and I will fix it.