Permutation group/Definition

Permutation group

For a set ${}M$, we call the set

${}\operatorname {Aut} \,(M)=\operatorname {Perm} \,(M)={\left\{\varphi :M\longrightarrow M\mid \varphi {\text{ bijective}}\right\}}\,$

of all bijective mappings on ${}M$ the automorphism group or the permutation group of ${}M$.