Transitive subgroup description rule

Definition
A subgroup description rule is said to be transitive if it satisfies the following two conditions:


 * Suppose $$G$$ is a group equipped with an encoding and $$K$$ is a subgroup of $$G$$ described by means of the subgroup description rule. Then, we can use this to obtain an encoding of $$K$$
 * If $$H$$ is a subgroup of $$K$$ described using the subgroup description rule inside $$K$$, then we can retrieve from this a description of $$H$$ as a subgroup of $$G$$, using the subgroup description rule

Further, we require that the algorithms for both be polynomial in the input sizes.