Category:Subgroup properties

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 $$G'$$.