DIHEDRAL TYPE on Z_N (E = {+-1}): all the relations commutative?
  N= 3: True
  N= 4: False
  N= 5: True
  N= 6: True
  N= 7: True
  N= 8: True
  N= 9: True
  N=10: True
  N=11: True
  N=12: True
  N=13: True
  N=14: True
  N=15: True
  N=16: True
  N=17: True
  N=18: True
  N=19: True
  N=20: True
PRIME CASE, p < 200: number of pairs (p,k) where all the relations are commutative,
  compared with the bound p > (k-1)(k-2)+2 of Theorem 8.2
  total 173, commutative 139, bound applies 97, violations of the bound: []
GENERAL CASE, N < 130, all the groups -1 in E generated by at most 3 elements, k = |E|, m = max gcd(a-1,N):
  all the relations must be commutative when N > mk(k-1)-2(k-2) (Theorem 8.2), and when N > 2(k-1)(km-1)+2 (Theorem 8.1)
  groups 512, commutative 371, Theorem 8.2 applies 183, Theorem 8.1 applies 158, violations: []
PRIME POWERS, E of order k | p-1:
  N=  9 k= 2: True
  N= 25 k= 2: True
  N= 25 k= 4: True
  N= 27 k= 2: True
  N= 49 k= 2: True
  N= 49 k= 6: True
  N=121 k= 2: True
  N=121 k=10: True
  N=125 k= 2: True
  N=125 k= 4: True
  N=169 k= 2: True
  N=169 k= 4: True
  N=169 k= 6: True
  N=169 k=12: True