The package pnqporc provides the methods to calculate generalized PORC polynomials in the indeterminates p and q enumerating the number of isomorphism types of groups of order p^nq for n ≤ 5 and different primes p and q.
These generalized PORC polynomials can contain expressions of the form d(s,t). When evaluating, the value of d(s,t) is 1 if s ∣ t and 0 otherwise.
Furthermore, the generalized PORC polynomials can contain expressions of the form g(p^m-1,q). When evaluating, the value of g(p^m-1,q) is 1 if m is minimal such that p^m-1 ∣ q and 0 otherwise.
For more details, we refer to the paper [EM17].
The following functions compute generalized PORC polynomials enumerating the number of isomorphism types of groups of order p^nq for n ≤ 5 (or certain subsets).
‣ NumberPNQ ( n ) | ( operation ) |
Given an integer n ≤ 5, this returns a generalized PORC polynomial in p and q enumerating the number of isomorphism types of groups of order p^nq.
‣ NumberPNQNormalPSylow ( n ) | ( operation ) |
Given an integer n ≤ 5, this returns a generalized PORC polynomial in p and q enumerating the number of isomorphism types of non-nilpotent groups of order p^nq with normal Sylow p-subgroup.
‣ NumberPNQNormalQSylow ( n ) | ( operation ) |
Given an integer n ≤ 5, this returns a generalized PORC polynomial in p and q enumerating the number of isomorphism types of non-nilpotent groups of order p^nq with normal Sylow q-subgroup.
‣ NumberPNQExceptional ( n ) | ( operation ) |
Given an integer n ≤ 5, this returns a generalized PORC polynomial in p and q enumerating the number of isomorphism types of non-nilpotent groups of order p^nq, which do not contain a normal Sylow subgroup.
‣ NumberPNQNilpotent ( n ) | ( operation ) |
Given an integer n ≤ 5, this returns a generalized PORC polynomial in p and q enumerating the number of isomorphism types of nilpotent groups of order p^nq. This coincides with the number of isomorphism types of groups of order p^n.
‣ EvalPNQPorcPoly ( poly, p, q ) | ( operation ) |
This evaluates a generalized PORC polynomial returned by one of the functions in the previous section at the given primes p and q.
generated by GAPDoc2HTML