The following function allows to compute nilpotent quotients for finitely presented associative \(Z\)-algebras given by a number of generators and relators.
‣ NilpotentQuotientFpZAlgebra ( A, c ) | ( operation ) |
Given a finitely presented associative \(Z\)-algebra, this function computes the class-c quotient.
Let \(I(G)\) denote the augmentation ideal of a group \(G\), then the following functions calculate the class-\(c\) quotient of \(I(G)\) for finitely presented groups and pcp-groups. One can further choose to print the additive structure of the augmentation quotients \(I(G)^i/I(G)^{i+1}\) during computation.
‣ AugmentationQuotientFpGroup ( G, c, print ) | ( operation ) |
Given a finitely presented group G, this function computes the class-c quotient of the augmentation ideal in the integral group ring \(Z\)G. If print is set to true, then the augmentation quotients are printed during computation.
‣ AugmentationQuotientPcpGroup ( G, c, print ) | ( operation ) |
Given a pcp-group G, this function computes the class-c quotient of the augmentation ideal in the integral group ring \(Z\)G. If print is set to true, then the augmentation quotients are printed during computation.
gap> H := HeisenbergPcpGroup(1);; gap> AugmentationQuotientPcpGroup(H, 5, true);; Q_1 = Z^2 Q_2 = Z^4 Q_3 = Z^6 Q_4 = Z^9 Q_5 = Z^12
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