| Quellcodebibliothek Statistik Leitseite products/Sources/formale Sprachen/GAP/pkg/nq/examples/ (Algebra von RWTH Aachen Version 4.15.1©) Datei vom 12.0.2024 mit Größe 14 kB |
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Quelle G3.out Sprache: unbekannt |
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# Calculating a nilpotent quotient # Nilpotency class: 20 # Size of exponents: 8 bytes # # Calculating the abelian quotient ... # The abelian quotient has 3 generators # with the following exponents: 0 0 0 # # Calculating the class 2 quotient ... ## Sizes: 3 6 # Maximal entry: 0 # Layer 2 of the lower central series has 2 generators # with the following exponents: 0 0 # # Calculating the class 3 quotient ... ## Sizes: 3 5 12 # Maximal entry: 0 # Layer 3 of the lower central series has 1 generators # with the following exponents: 0 # # Calculating the class 4 quotient ... ## Sizes: 3 5 6 15 # Maximal entry: 0 # Layer 4 of the lower central series has 1 generators # with the following exponents: 2 # # Calculating the class 5 quotient ... ## Sizes: 3 5 6 7 19 # Maximal entry: 1 # Layer 5 of the lower central series has 2 generators # with the following exponents: 2 2 # # Calculating the class 6 quotient ... ## Sizes: 3 5 6 7 9 27 # Maximal entry: 4 # Layer 6 of the lower central series has 1 generators # with the following exponents: 2 # # Calculating the class 7 quotient ... ## Sizes: 3 5 6 7 9 10 31 # Maximal entry: 4 # Layer 7 of the lower central series has 1 generators # with the following exponents: 2 # # Calculating the class 8 quotient ... ## Sizes: 3 5 6 7 9 10 11 35 # Maximal entry: 5 # Layer 8 of the lower central series has 1 generators # with the following exponents: 2 # # Calculating the class 9 quotient ... ## Sizes: 3 5 6 7 9 10 11 12 39 # Maximal entry: 4 # Layer 9 of the lower central series has 1 generators # with the following exponents: 2 # # Calculating the class 10 quotient ... ## Sizes: 3 5 6 7 9 10 11 12 13 43 # Maximal entry: 18 # Layer 10 of the lower central series has 1 generators # with the following exponents: 2 # # Calculating the class 11 quotient ... ## Sizes: 3 5 6 7 9 10 11 12 13 14 47 # Maximal entry: 11 # Layer 11 of the lower central series has 1 generators # with the following exponents: 2 # # Calculating the class 12 quotient ... ## Sizes: 3 5 6 7 9 10 11 12 13 14 15 51 # Maximal entry: 12 # Layer 12 of the lower central series has 1 generators # with the following exponents: 2 # # Calculating the class 13 quotient ... ## Sizes: 3 5 6 7 9 10 11 12 13 14 15 16 55 # Maximal entry: 15 # Layer 13 of the lower central series has 1 generators # with the following exponents: 2 # # Calculating the class 14 quotient ... ## Sizes: 3 5 6 7 9 10 11 12 13 14 15 16 17 59 # Maximal entry: 20 # Layer 14 of the lower central series has 1 generators # with the following exponents: 2 # # Calculating the class 15 quotient ... ## Sizes: 3 5 6 7 9 10 11 12 13 14 15 16 17 18 63 # Maximal entry: 30 # Layer 15 of the lower central series has 1 generators # with the following exponents: 2 # # Calculating the class 16 quotient ... ## Sizes: 3 5 6 7 9 10 11 12 13 14 15 16 17 18 19 67 # Maximal entry: 44 # Layer 16 of the lower central series has 1 generators # with the following exponents: 2 # # Calculating the class 17 quotient ... ## Sizes: 3 5 6 7 9 10 11 12 13 14 15 16 17 18 19 20 71 # Maximal entry: 52 # Layer 17 of the lower central series has 1 generators # with the following exponents: 2 # # Calculating the class 18 quotient ... ## Sizes: 3 5 6 7 9 10 11 12 13 14 15 16 17 18 19 20 21 75 # Maximal entry: 175 # Layer 18 of the lower central series has 1 generators # with the following exponents: 2 # # Calculating the class 19 quotient ... ## Sizes: 3 5 6 7 9 10 11 12 13 14 15 16 17 18 19 20 21 22 79 # Maximal entry: 175 # Layer 19 of the lower central series has 1 generators # with the following exponents: 2 # # Calculating the class 20 quotient ... ## Sizes: 3 5 6 7 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 83 # Maximal entry: 434 # Layer 20 of the lower central series has 1 generators # with the following exponents: 2 # # The epimorphism : # e1 |---> A # e2 |---> B # e3 |---> C # The nilpotent quotient : <A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X | G^2 = H*I*L, H^2 = K*L*M*N*O*P*Q*R*S*T*U*V*W*X, I^2 = K, J^2 = L, K^2 = M, L^2 = N, M^2 = O, N^2 = P, O^2 = Q, P^2 = R, Q^2 = S, R^2 = T, S^2 = U, T^2 = V, U^2 = W, V^2 = X, W^2, X^2, B^A =: B*D, B^(A^-1) = B*D^-1, C^A = C, C^(A^-1) = C, C^B =: C*E, C^(B^-1) = C*E^-1, D^A = D, D^(A^-1) = D, D^B = D, D^(B^-1) = D, D^C = D*F^-1*G*J*L*N*P*R*T*V*X, D^(C^-1) = D*F*G*H*J*K, E^A =: E*F, E^(A^-1) = E*F^-1*H, E^B = E, E^(B^-1) = E, E^C = E, E^(C^-1) = E, E^D = E*G*I*J*K*L*M*N*O*P*Q*R*S*T*U*V*W*X, E^(D^-1) = E*G*H, F^A = F*H*K*L, F^(A^-1) = F*H*K*L, F^B =: F*G, F^(B^-1) = F*G*H*I*J, F^C = F, F^(C^-1) = F, F^D = F*H*K*L, F^(D^-1) = F*H*K*L, F^E = F*I*J, F^(E^-1) = F*I*J, G^A =: G*H, G^(A^-1) = G*H, G^B = G*J*L*N*P*R*T*V*X, G^(B^-1) = G*J*L*N*P*R*T*V*X, G^C =: G*I, G^(C^-1) = G*I, G^D = G*J*L*N*P*R*T*V*X, G^(D^-1) = G*J*L*N*P*R*T*V*X, G^E = G*J*L*N*P*R*T*V*X, G^(E^-1) = G*J*L*N*P*R*T*V*X, G^F = G, G^(F^-1) = G, H^A = H*K*L, H^(A^-1) = H*K*L, H^B = H*J, H^(B^-1) = H*J, H^C = H, H^(C^-1) = H, H^D = H*K*L, H^(D^-1) = H*K*L, H^E = H*K*L, H^(E^-1) = H*K*L, H^F = H, H^(F^-1) = H, H^G = H, I^A = I, I^(A^-1) = I, I^B =: I*J, I^(B^-1) = I*J, I^C = I*K*M*O*Q*S*U*W, I^(C^-1) = I*K*M*O*Q*S*U*W, I^D = I*K*M*O*Q*S*U*W, I^(D^-1) = I*K*M*O*Q*S*U*W, I^E = I*K*M*O*Q*S*U*W, I^(E^-1) = I*K*M*O*Q*S*U*W, I^F = I, I^(F^-1) = I, I^G = I, I^H = I, J^A = J*K*L*M*N*O*P*Q*R*S*T*U*V*W*X, J^(A^-1) = J*K*L*M*N*O*P*Q*R*S*T*U*V*W*X, J^B = J*L*N*P*R*T*V*X, J^(B^-1) = J*L*N*P*R*T*V*X, J^C =: J*K, J^(C^-1) = J*K, J^D = J*L*N*P*R*T*V*X, J^(D^-1) = J*L*N*P*R*T*V*X, J^E = J*L*N*P*R*T*V*X, J^(E^-1) = J*L*N*P*R*T*V*X, J^F = J, J^(F^-1) = J, J^G = J, J^H = J, J^I = J, K^A = K, K^(A^-1) = K, K^B =: K*L, K^(B^-1) = K*L, K^C = K*M*O*Q*S*U*W, K^(C^-1) = K*M*O*Q*S*U*W, K^D = K*M*O*Q*S*U*W, K^(D^-1) = K*M*O*Q*S*U*W, K^E = K*M*O*Q*S*U*W, K^(E^-1) = K*M*O*Q*S*U*W, K^F = K, K^(F^-1) = K, K^G = K, K^H = K, K^I = K, K^J = K, L^A = L*M*N*O*P*Q*R*S*T*U*V*W*X, L^(A^-1) = L*M*N*O*P*Q*R*S*T*U*V*W*X, L^B = L*N*P*R*T*V*X, L^(B^-1) = L*N*P*R*T*V*X, L^C =: L*M, L^(C^-1) = L*M, L^D = L*N*P*R*T*V*X, L^(D^-1) = L*N*P*R*T*V*X, L^E = L*N*P*R*T*V*X, L^(E^-1) = L*N*P*R*T*V*X, L^F = L, L^(F^-1) = L, L^G = L, L^H = L, L^I = L, L^J = L, L^K = L, M^A = M, M^(A^-1) = M, M^B =: M*N, M^(B^-1) = M*N, M^C = M*O*Q*S*U*W, M^(C^-1) = M*O*Q*S*U*W, M^D = M*O*Q*S*U*W, M^(D^-1) = M*O*Q*S*U*W, M^E = M*O*Q*S*U*W, M^(E^-1) = M*O*Q*S*U*W, M^F = M, M^(F^-1) = M, M^G = M, M^H = M, M^I = M, M^J = M, M^K = M, M^L = M, N^A = N*O*P*Q*R*S*T*U*V*W*X, N^(A^-1) = N*O*P*Q*R*S*T*U*V*W*X, N^B = N*P*R*T*V*X, N^(B^-1) = N*P*R*T*V*X, N^C =: N*O, N^(C^-1) = N*O, N^D = N*P*R*T*V*X, N^(D^-1) = N*P*R*T*V*X, N^E = N*P*R*T*V*X, N^(E^-1) = N*P*R*T*V*X, N^F = N, N^(F^-1) = N, N^G = N, N^H = N, N^I = N, N^J = N, N^K = N, N^L = N, N^M = N, O^A = O, O^(A^-1) = O, O^B =: O*P, O^(B^-1) = O*P, O^C = O*Q*S*U*W, O^(C^-1) = O*Q*S*U*W, O^D = O*Q*S*U*W, O^(D^-1) = O*Q*S*U*W, O^E = O*Q*S*U*W, O^(E^-1) = O*Q*S*U*W, O^F = O, O^(F^-1) = O, O^G = O, O^H = O, O^I = O, O^J = O, O^K = O, O^L = O, O^M = O, P^A = P*Q*R*S*T*U*V*W*X, P^(A^-1) = P*Q*R*S*T*U*V*W*X, P^B = P*R*T*V*X, P^(B^-1) = P*R*T*V*X, P^C =: P*Q, P^(C^-1) = P*Q, P^D = P*R*T*V*X, P^(D^-1) = P*R*T*V*X, P^E = P*R*T*V*X, P^(E^-1) = P*R*T*V*X, P^F = P, P^(F^-1) = P, P^G = P, P^H = P, P^I = P, P^J = P, P^K = P, P^L = P, Q^A = Q, Q^(A^-1) = Q, Q^B =: Q*R, Q^(B^-1) = Q*R, Q^C = Q*S*U*W, Q^(C^-1) = Q*S*U*W, Q^D = Q*S*U*W, Q^(D^-1) = Q*S*U*W, Q^E = Q*S*U*W, Q^(E^-1) = Q*S*U*W, Q^F = Q, Q^(F^-1) = Q, Q^G = Q, Q^H = Q, Q^I = Q, Q^J = Q, Q^K = Q, R^A = R*S*T*U*V*W*X, R^(A^-1) = R*S*T*U*V*W*X, R^B = R*T*V*X, R^(B^-1) = R*T*V*X, R^C =: R*S, R^(C^-1) = R*S, R^D = R*T*V*X, R^(D^-1) = R*T*V*X, R^E = R*T*V*X, R^(E^-1) = R*T*V*X, R^F = R, R^(F^-1) = R, R^G = R, R^H = R, R^I = R, R^J = R, S^A = S, S^(A^-1) = S, S^B =: S*T, S^(B^-1) = S*T, S^C = S*U*W, S^(C^-1) = S*U*W, S^D = S*U*W, S^(D^-1) = S*U*W, S^E = S*U*W, S^(E^-1) = S*U*W, S^F = S, S^(F^-1) = S, S^G = S, S^H = S, S^I = S, T^A = T*U*V*W*X, T^(A^-1) = T*U*V*W*X, T^B = T*V*X, T^(B^-1) = T*V*X, T^C =: T*U, T^(C^-1) = T*U, T^D = T*V*X, T^(D^-1) = T*V*X, T^E = T*V*X, T^(E^-1) = T*V*X, T^F = T, T^(F^-1) = T, T^G = T, U^A = U, U^(A^-1) = U, U^B =: U*V, U^(B^-1) = U*V, U^C = U*W, U^(C^-1) = U*W, U^D = U*W, U^(D^-1) = U*W, U^E = U*W, U^(E^-1) = U*W, U^F = U, U^(F^-1) = U, V^A = V*W*X, V^(A^-1) = V*W*X, V^B = V*X, V^(B^-1) = V*X, V^C =: V*W, V^(C^-1) = V*W, V^D = V*X, V^(D^-1) = V*X, V^E = V*X, V^(E^-1) = V*X, W^A = W, W^(A^-1) = W, W^B =: W*X, W^(B^-1) = W*X, W^C = W, W^(C^-1) = W > # Class : 20 # Nr of generators of each class : 3 2 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 # The definitions: # D := [ B, A ] # E := [ C, B ] # F := [ C, B, A ] # G := [ C, B, A, B ] # H := [ C, B, A, B, A ] # I := [ C, B, A, B, C ] # J := [ C, B, A, B, C, B ] # K := [ C, B, A, B, C, B, C ] # L := [ C, B, A, B, C, B, C, B ] # M := [ C, B, A, B, C, B, C, B, C ] # N := [ C, B, A, B, C, B, C, B, C, B ] # O := [ C, B, A, B, C, B, C, B, C, B, C ] # P := [ C, B, A, B, C, B, C, B, C, B, C, B ] # Q := [ C, B, A, B, C, B, C, B, C, B, C, B, C ] # R := [ C, B, A, B, C, B, C, B, C, B, C, B, C, B ] # S := [ C, B, A, B, C, B, C, B, C, B, C, B, C, B, C ] # T := [ C, B, A, B, C, B, C, B, C, B, C, B, C, B, C, B ] # U := [ C, B, A, B, C, B, C, B, C, B, C, B, C, B, C, B, C ] # V := [ C, B, A, B, C, B, C, B, C, B, C, B, C, B, C, B, C, B ] # W := [ C, B, A, B, C, B, C, B, C, B, C, B, C, B, C, B, C, B, C ] # X := [ C, B, A, B, C, B, C, B, C, B, C, B, C, B, C, B, C, B, C, B ] [ Dauer der Verarbeitung: 0.18 Sekunden (vorverarbeitet) ] |
2026-03-28