Cohomology and profinite topologies for solvable groups of finite rank

Assume $G$ is a solvable group whose elementary abelian sections are all finite. Suppose, further, that $p$ is a prime such that $G$ fails to contain any subgroups isomorphic to $C_{p^\infty}$. We show that if $G$ is nilpotent, then the pro-$p$ completion map $G\to \hat{G}_p$ induces an isomorphism $H^\ast(\hat{G}_p,M)\to H^\ast(G,M)$ for any discrete $\hat{G}_p$-module $M$ of finite $p$-power order. For the general case, we prove that $G$ contains a normal subgroup $N$ of finite index such that the map $H^\ast(\hat{N}_p,M)\to H^\ast(N,M)$ is an isomorphism for any discrete $\hat{N}_p$-module $M$ of finite $p$-power order. Moreover, if $G$ lacks any $C_{p^\infty}$-sections, the subgroup $N$ enjoys some additional special properties with respect to its pro-$p$ topology.Comment: This paper supersedes arXiv:1009.2645v5: the two theorems in the introduction to the latter paper are both corollaries to Theorem 1.1 in the present paper. In the second version, Theorem 1.1 is expressed in a slightly more general form than in the first versio

The quarter-point quadratic isoparametric element as a singular element for crack problems

The quadratic isoparametric elements which embody the inverse square root singularity are used for calculating the stress intensity factors at tips of cracks. The strain singularity at a point or an edge is obtained in a simple manner by placing the mid-side nodes at quarter points in the vicinity of the crack tip or an edge. These elements are implemented in NASTRAN as dummy elements. The method eliminates the use of special crack tip elements and in addition, these elements satisfy the constant strain and rigid body modes required for convergence

A Synthesis of Reinforcement Learning

Unified read-write modalities have led to many ex- tensive advances, including SCSI disks and multi-processors. In fact, few electrical engineers would disagree with the investigation of model checking, demonstrates the private importance of artificial in- telligence. We motivate an analysis of write-back caches, which we call Fest

The strong Atiyah conjecture for right-angled Artin and Coxeter groups

We prove the strong Atiyah conjecture for right-angled Artin groups and right-angled Coxeter groups. More generally, we prove it for groups which are certain finite extensions or elementary amenable extensions of such groups.Comment: Minor change