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

Groups with the same cohomology as their pro-pp completions

For any prime $p$ and group $G$, denote the pro-$p$ completion of $G$ by $\hat{G}^p$. Let $\mathcal{C}$ be the class of all groups $G$ such that, for each natural number $n$ and prime number $p$, $H^n(\hat{G^p},\mathbb Z/p)\cong H^n(G, \mathbb Z/p)$, where $\mathbb Z/p$ is viewed as a discrete, trivial $\hat{G}^p$-module. In this article we identify certain kinds of groups that lie in $\mathcal{C}$. In particular, we show that right-angled Artin groups are in $\mathcal{C}$ and that this class also contains some special types of free products with amalgamation.Comment: The revisions in the second version pertain to the exposition: the proof of Prop. 1.1, in particular, now includes more details. The third version includes a proof that right-angled Artin groups are residually $p$-finite for every prime $p

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

Illustrations of accounting for postemployment benefits : a survey of the application of FASB statement no. 112; Financial report survey, 54

https://egrove.olemiss.edu/aicpa_news/1216/thumbnail.jp

Illustrations of disclosures about fair value of financial instruments : a survey of the application of FASB statement no. 107; Financial report survey, 53

https://egrove.olemiss.edu/aicpa_news/1215/thumbnail.jp