alternating group is a normal subgroup of the symmetric group
Remark. What we have shown in the theorem is that, in fact, has index in . In general, if a subgroup of has index , then is normal in . (Since , there is an element , so that and thus ).
|Title||alternating group is a normal subgroup of the symmetric group|
|Date of creation||2013-03-22 13:42:32|
|Last modified on||2013-03-22 13:42:32|
|Last modified by||CWoo (3771)|