#
#    The ANU Nilpotent Quotient Program (Version 2.0 July 2002)
#    Calculating a nilpotent quotient
#    Nilpotency class: 11
#    Size of exponents: 8 bytes
#
#    Calculating the abelian quotient ...
#    The abelian quotient has 2 generators
#        with the following exponents: 0 0
#
#    Calculating the class 2 quotient ...
##  Sizes:  2  3
#    Layer 2 of the lower central series has 1 generators
#          with the following exponents: 0
#
#    Calculating the class 3 quotient ...
##  Sizes:  2  3  5
#    Maximal entry: 0
#    Layer 3 of the lower central series has 1 generators
#          with the following exponents: 0
#
#    Calculating the class 4 quotient ...
##  Sizes:  2  3  4  7
#    Maximal entry: 0
#    Layer 4 of the lower central series has 1 generators
#          with the following exponents: 0
#
#    Calculating the class 5 quotient ...
##  Sizes:  2  3  4  5  9
#    Maximal entry: 0
#    Layer 5 of the lower central series has 1 generators
#          with the following exponents: 0
#
#    Calculating the class 6 quotient ...
##  Sizes:  2  3  4  5  6  11
#    Maximal entry: 0
#    Layer 6 of the lower central series has 1 generators
#          with the following exponents: 2
#
#    Calculating the class 7 quotient ...
##  Sizes:  2  3  4  5  6  7  14
#    Maximal entry: 0
#    Layer 7 of the lower central series has 2 generators
#          with the following exponents: 2 2
#
#    Calculating the class 8 quotient ...
##  Sizes:  2  3  4  5  6  7  9  20
#    Maximal entry: 2
#    Layer 8 of the lower central series has 2 generators
#          with the following exponents: 2 2
#
#    Calculating the class 9 quotient ...
##  Sizes:  2  3  4  5  6  7  9  11  26
#    Maximal entry: 4
#    Layer 9 of the lower central series has 2 generators
#          with the following exponents: 2 2
#
#    Calculating the class 10 quotient ...
##  Sizes:  2  3  4  5  6  7  9  11  13  32
#    Maximal entry: 4
#    Layer 10 of the lower central series has 1 generators
#          with the following exponents: 2
#
#    Calculating the class 11 quotient ...
##  Sizes:  2  3  4  5  6  7  9  11  13  14  35
#    Integer matrix is the identity.
#    Maximal entry: 5


#    The epimorphism :
#    e1 |---> A
#    e2 |---> B


#    The nilpotent quotient :
    <A,B,C,D,E,F,G,H,I,J,K,L,M,N
      |
        G^2 = H*I*J*K*L*M,
        H^2 = K,
        I^2 = J*M*N,
        J^2 = M,
        K^2 = L,
        L^2,
        M^2 = N,
        N^2,
        B^A           =: B*C,
        B^(A^-1)      =  B*C^-1,
        C^A           =  C,
        C^(A^-1)      =  C,
        C^B           =: C*D,
        C^(B^-1)      =  C*D^-1*E*J,
        D^A           =  D*F*K*L,
        D^(A^-1)      =  D*F^-1*H*L,
        D^B           =: D*E,
        D^(B^-1)      =  D*E^-1*I,
        D^C           =  D*F*K*L,
        D^(C^-1)      =  D*F^-1*H*L,
        E^A           =: E*F,
        E^(A^-1)      =  E*F^-1*H*K,
        E^B           =  E*I,
        E^(B^-1)      =  E*I*J,
        E^C           =  E*G*I*J*K*L*M,
        E^(C^-1)      =  E*G*H*M*N,
        E^D           =  E*I,
        E^(D^-1)      =  E*I*J,
        F^A           =  F*H*K*L,
        F^(A^-1)      =  F*H*L,
        F^B           =: F*G,
        F^(B^-1)      =  F*G*H*J*N,
        F^C           =  F*H*K*L,
        F^(C^-1)      =  F*H*L,
        F^D           =  F*K*M,
        F^(D^-1)      =  F*K*L*M*N,
        F^E           =  F*M,
        F^(E^-1)      =  F*M*N,
        G^A           =: G*H,
        G^(A^-1)      =  G*H*K,
        G^B           =: G*I,
        G^(B^-1)      =  G*I*J,
        G^C           =  G*J*K*L*N,
        G^(C^-1)      =  G*J*K*M*N,
        G^D           =  G,
        G^(D^-1)      =  G,
        G^E           =  G,
        G^(E^-1)      =  G,
        H^A           =  H*L,
        H^(A^-1)      =  H*L,
        H^B           =: H*J,
        H^(B^-1)      =  H*J*M*N,
        H^C           =  H*L,
        H^(C^-1)      =  H*L,
        H^D           =  H,
        H^(D^-1)      =  H,
        I^A           =: I*K,
        I^(A^-1)      =  I*K*L,
        I^B           =  I,
        I^(B^-1)      =  I,
        I^C           =  I*M*N,
        I^(C^-1)      =  I*M,
        I^D           =  I,
        I^(D^-1)      =  I,
        J^A           =: J*L,
        J^(A^-1)      =  J*L,
        J^B           =  J,
        J^(B^-1)      =  J,
        J^C           =  J*N,
        J^(C^-1)      =  J*N,
        K^A           =  K,
        K^(A^-1)      =  K,
        K^B           =: K*M,
        K^(B^-1)      =  K*M*N,
        K^C           =  K,
        K^(C^-1)      =  K,
        L^A           =  L,
        L^(A^-1)      =  L,
        L^B           =: L*N,
        L^(B^-1)      =  L*N,
        M^A           =  M,
        M^(A^-1)      =  M,
        M^B           =  M,
        M^(B^-1)      =  M >

#    Class : 10
#    Nr of generators of each class : 2 1 1 1 1 1 2 2 2 1


#    The definitions:
#    C := [ B, A ]
#    D := [ B, A, B ]
#    E := [ B, A, B, B ]
#    F := [ B, A, B, B, A ]
#    G := [ B, A, B, B, A, B ]
#    H := [ B, A, B, B, A, B, A ]
#    I := [ B, A, B, B, A, B, B ]
#    J := [ B, A, B, B, A, B, A, B ]
#    K := [ B, A, B, B, A, B, B, A ]
#    L := [ B, A, B, B, A, B, A, B, A ]
#    M := [ B, A, B, B, A, B, B, A, B ]
#    N := [ B, A, B, B, A, B, A, B, A, B ]
