Artin L-function

Subgroup properties are properties of subgroups of a group. These properties are assumed to satisfy only one condition : they must be invariant up to commuting isomorphism. That is, if $G$ and $G'$ are isomorphic groups, and $H$ is a subgroup of $G$ whose image under the isomorphism is $H'$ then $H$ has the property in $G$ if and only if $H'$ has the property in $G'$.