Approximating the Schur multiplier of certain infinitely presented groups via nilpotent quotients

A Nilpotent Quotient Algorithm for Certain Infinitely Presented Groups and its Applications

We describe a nilpotent quotient algorithm for a certain type of infinite presentations: the so-called finite L-presentations. We then exhibit finite L-presentations for various interesting groups and report on the application of our nilpotent quotient algorithm to them. As result, we obtain conjectural descriptions of the lower central series structure of various interesting groups including t...

nilpotent quotients of L - presented groups A GAP 4 package

Fitting quotients of finitely presented abelian-by-nilpotent groups

We show that every finitely generated nilpotent group of class 2 occurs as the quotient of a finitely presented abelian-by-nilpotent group by its largest nilpotent normal subgroup.

nilpotent quotients in finitely presented Lie rings †

A nilpotent quotient algorithm for finitely presented Lie rings over Z (LIENQ) is described. The paper studies the graded and non-graded cases separately. The algorithm computes the so-called nilpotent presentation for a finitely presented, nilpotent Lie ring. A nilpotent presentation consists of generators for the abelian group and the products expressed as linear combinations for pairs formed...

A restriction on the Schur multiplier of nilpotent Lie algebras

An improvement of a bound of Yankosky (2003) is presented in this paper, thanks to a restriction which has been recently obtained by the authors on the Schur multiplier M(L) of a finite dimensional nilpotent Lie algebra L. It is also described the structure of all nilpotent Lie algebras such that the bound is attained. An important role is played by the presence of a derived subalgebra of maxim...