Finite generation of nilpotent quotients of fundamental groups of punctured spectra

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.

Completed representation ring spectra of nilpotent groups

In this paper, we examine the “derived completion” of the representation ring of a pro-p group G∧ p with respect to an augmentation ideal. This completion is no longer a ring: it is a spectrum with the structure of a module spectrum over the Eilenberg–MacLane spectrum HZ , and can have higher homotopy information. In order to explain the origin of some of these higher homotopy classes, we defin...

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.

-distortion of Finite Quotients of Amenable Groups

We study the Lp-distortion of finite quotients of amenable groups. In particular, for every 2 ≤ p < ∞, we prove that the lp-distortions of the groups C2 ≀Cn and Cpn ⋉Cn are in Θ((log n) 1/p), and that the lp-distortion of C2 n ⋉A Z, where A is the matrix (