TheR∞property for nilpotent quotients of surface groups

Maximal Nilpotent Quotients of 3-manifold Groups

We show that if the lower central series of the fundamental group of a closed oriented 3-manifold stabilizes then the maximal nilpotent quotient is a cyclic group, a quaternion 2-group cross an odd order cyclic group, or a Heisenberg group. These groups are well known to be precisely the nilpotent fundamental groups of closed oriented 3-manifolds.

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.

Computing twisted conjugacy classes in free groups using nilpotent quotients

There currently exists no algebraic algorithm for computing twisted conjugacy classes in free groups. We propose a new technique for deciding twisted conjugacy relations using nilpotent quotients. Our technique is a generalization of the common abelianization method, but admits significantly greater rates of success. We present experimental results demonstrating the efficacy of the technique, a...

Some Inequalities for Nilpotent Multipliers of Powerful p-Groups