alternating group has index 2 in the symmetric group, the
We prove that the alternating group has index 2 in the symmetric group , i.e., has the same cardinality as its complement . The proof is function-theoretic. Its idea is similar to the proof in the parent topic, but the focus is less on algebraic aspect.
Let . Define by , where is the product of and .
since exists and .
Onto: Given , there exists an element in , namely , such that
|Title||alternating group has index 2 in the symmetric group, the|
|Date of creation||2013-03-22 16:48:49|
|Last modified on||2013-03-22 16:48:49|
|Last modified by||yesitis (13730)|