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{{r|Normal subgroup}}

...'' and denoted <math>A_{n}</math>. In fact, <math>A_{n}</math> is always a normal subgroup of <math>S_{n}</math>. ...is <math>A_{n}</math>, unless n=4. When n=4, there is an additional proper normal subgroup, often denoted V, consisting of the identity permutation and the permutatio

...t that does not contain the identity element ''e'' cannot be a group). A [[normal subgroup]] is a very important kind of subgroup and is defined by a few different eq ...map to the identity element; this set is a [[normal subgroup]], and every normal subgroup is the kernel of some homomorphism.

...}</math> must have degree a power of 2. Its [[Galois group]] must have a [[normal subgroup]] of [[index of a subgroup|index]] 2, but a generating element must already

#Given a group ''G'' and a [[normal subgroup]] ''N'', the ''[[quotient group]]'' is the set of [[coset]]s of ''G/N'' tog