Distortion of wreath products in some finitely presented groups

Wreath products such as Z wr Z are not finitely-presentable yet can occur as subgroups of finitely presented groups. Here we compute the distortion of Z wr Z as a subgroup of Thompson's group F and as a subgroup of Baumslag's metabelian group G. We find that Z wr Z is undistorted in F but is at least exponentially distorted in G.Comment: 9 pages, 5 figure

Electronic Recording of Police Interrogations

Policy recommendation: All Virginia state law enforcement agencies to adopt a written department policy requiring electronic recording of any custodial interrogation conducted in a place of detention

A Wolf in Sheep’s Clothing: The Unilateral Executive and the Separation of Powers

[Excerpt] “The United States Constitution vests all executive powers in a president. This is the unitary executive theory. By virtue of this, many believe the president is vested with the power to act unilaterally. This is the unilateral executive theory. However, the unilateral executive portends more than action. In reality, the unilateral executive theory provides an opportunity to implement a unilateral agenda. Thus, the aim of this paper is to consider executive power, the separation of powers, and the unilateral executive theory to determine if presidential power under the separation of powers doctrine is actually “a wolf in sheep’s clothing.” With regard to this, we will consider the intentions of the framers, the text of the Constitution, and the mandates of governmental necessity.

Critical literacy as an approach to literary study in the multicultural, high-school classroom

As an approach to literary study, critical literacy is not a widespread practice in New Zealand secondary schools. This article draws on a major project on teaching literature in the multicultural classroom that take place over two years in 2008-2009. In it we report on a case study where a Year 13 English teacher designed and tested a novel English programme with a reputedly less able and culturally diverse group of final-year students entitled “13 English – Popular Culture”. In it, she guided her students through a range of reading tasks aimed at developing in her students an awareness of ways in which texts position readers to take up certain meanings and not others through the language used. Over the course of the programme, students moved from compliant readers to readers who were sensitized to the manipulative power of texts. They enjoyed being exposed to a variety of theme-related texts, especially when these empowered them by enabling them to deploy their own cultural resources in responding to and challenging the texts they encountered. Students needed careful scaffolding in respect of metalinguistic understanding in order to be able to discuss the specific ways in which language constructs meaning. Indeed, these students struggled with this aspect of a critical literacy approach. However, despite the fact that these students were engaged in high-stakes assessment at a higher level than in the previous year, all gained more NCEA credits than they had in Year 12

Bounding right-arm rotation distances

Rotation distance measures the difference in shape between binary trees of the same size by counting the minimum number of rotations needed to transform one tree to the other. We describe several types of rotation distance where restrictions are put on the locations where rotations are permitted, and provide upper bounds on distances between trees with a fixed number of nodes with respect to several families of these restrictions. These bounds are sharp in a certain asymptotic sense and are obtained by relating each restricted rotation distance to the word length of elements of Thompson's group F with respect to different generating sets, including both finite and infinite generating sets.Comment: 30 pages, 11 figures. This revised version corrects some typos and has some clearer proofs of the results for the lower bounds and better figure

Thompson's group F is not almost convex

We show that Thompson's group F does not satisfy Cannon's almost convexity condition AC(n) for any integer n in the standard finite two generator presentation. To accomplish this, we construct a family of pairs of elements at distance n from the identity and distance 2 from each other, which are not connected by a path lying inside the n-ball of length less than k for increasingly large k. Our techniques rely upon Fordham's method for calculating the length of a word in F and upon an analysis of the generators' geometric actions on the tree pair diagrams representing elements of F.Comment: 19 pages, 7 figure