Editing Symmetric group (section)

=== Verification of group axioms ===
To check that the symmetric group on a set ''X'' is indeed a [[group (mathematics)|group]], it is necessary to verify the group axioms of closure, associativity, identity, and inverses.<ref>{{cite book |last1=Vasishtha |first1=A.R. |last2=Vasishtha |first2=A.K. |chapter=2. Groups S3 Group Definition |chapter-url={{GBurl|45eCTUS6YnQC|p=49}} |title=Modern Algebra |publisher=Krishna Prakashan Media |date=2008 |isbn=9788182830561 |pages=49 }}</ref>
# The operation of function composition is closed in the set of permutations of the given set ''X''.
# Function composition is always associative.
# The trivial bijection that assigns each element of ''X'' to itself serves as an identity for the group.
# Every bijection has an [[inverse function]] that undoes its action, and thus each element of a symmetric group does have an inverse which is a permutation too.