The Outer Automorphism Groups of Two-Generator One-Relator Groups with Torsion

The main result of this paper is a complete classification of the outer automorphism groups of two-generator, one-relator groups with torsion. To this classification we apply recent algorithmic results of Dahmani--Guirardel, which yields an algorithm to compute the isomorphism class of the outer automorphism group of a given two-generator, one-relator group with torsion.Comment: 15 pages, final version. To appear in Proc. Amer. Math. So

On the outer automorphism groups of finitely generated, residually finite groups

Bumagin-Wise posed the question of whether every countable group can be realised as the outer automorphism group of a finitely generated, residually finite group. We give a partial answer to this problem for recursively presentable groups.Comment: 13 pages. Final versio

Every group is the outer automorphism group of an HNN-extension of a fixed triangle group

Fix an equilateral triangle group $T_i=\langle a, b; a^i, b^i, (ab)^i\rangle$ with $i\geq6$ arbitrary. Our main result is: for every presentation $\mathcal{P}$ of every countable group $Q$ there exists an HNN-extension $T_{\mathcal{P}}$ of $T_i$ such that $\operatorname{Out}(T_{\mathcal{P}})\cong Q$. We construct the HNN-extensions explicitly, and examples are given. The class of groups constructed have nice categorical and residual properties. In order to prove our main result we give a method for recognising malnormal subgroups of small cancellation groups, and we introduce the concept of "malcharacteristic" subgroups.Comment: 39 pages. Final version, to appear in Advances in Mathematic

On a question of Bumagin and Wise

Motivated by a question of Bumagin and Wise, we construct a continuum of finitely generated, residually finite groups whose outer automorphism groups are pairwise non-isomorphic finitely generated, non-recursively-presentable groups. These are the first examples of such residually finite groups.Comment: 8 page

Factor Endowments and the Returns to Skill: New Evidence from the American Past

The existing literature on skill-biased technical change has not considered how the technological endowment itself plays a role in the returns to skill. This paper constructs a simple model of skill biased technical change which highlights the role that resource endowments play in the returns to education. The model predicts variation in returns to education with skill biased technological change if there is significant heterogeneity in resource endowments before the technological change. Using a variety of historical sources, we document the heterogeneous technology levels by region in the American past. We then estimate the returns to education of high school teachers in the early twentieth century using a new data source. a report from the U.S. Commissioner of Education in 1909. Overall, we find significant regional variation in the returns to education that match differences in resource endowments, with large (within-occupation) returns for the Midwest and Southwest (7%), but much lower returns in the South (3%) and West (0.5%). We also show that our results are generalizable to returns to education in the United States and that returns to education for teachers tracked quite closely with the overall returns to education from 1940 onward.

On the Heterogeneity of Dowry Motives

Dowries have been modeled as pre-mortem bequests to daughters or as groom-prices paid to in-laws. These two classes of models yield mutually exclusive predictions, but empirical tests of these predictions have been mixed. We argue that the heterogeneity of findings can be explained by a heterogeneous world--some households use dowries as a bequest and others use dowries as a price. We estimate a model with heterogeneous dowry motives and use the predictions from the competing theories in an exogenous switching regression to place households in the price or bequest regime. Our empirical strategy generates multiple, independent checks on the validity of regime assignment. Using retrospective marriage data from rural Bangladesh, we find robust evidence of heterogeneity in dowry motives in the population; that bequest dowries have declined in prevalence and amount over time; and that bequest households are better off compared to price households on a variety of welfare measures.

A spin-dependent local moment approach to the Anderson impurity model

We present an extension of the local moment approach to the Anderson impurity model with spin-dependent hybridization. By employing the two-self-energy description, as originally proposed by Logan and co-workers, we applied the symmetry restoration condition for the case with spin-dependent hybridization. Self-consistent ground states were determined through variational minimization of the ground state energy. The results obtained with our spin-dependent local moment approach applied to a quantum dot system coupled to ferromagnetic leads are in good agreement with those obtained from previous work using numerical renormalization group calculations

Whoa, Nellie! Empirical Tests of College Football's Conventional Wisdom

College football fans, coaches, and observers have adopted a set of beliefs about how college football poll voters behave. I document three pieces of conventional wisdom in college football regarding the timing of wins and losses, the value of playing strong opponents, and the value of winning by wide margins. Using a unique data set with 25 years of AP poll results, I test college football's conventional wisdom. In particular, I test (1) whether it is better to lose early or late in the season, (2) whether teams benefit from playing stronger opponents, and (3) whether teams are rewarded for winning by large margins. Contrary to conventional wisdom, I find that (1) it is better to lose later in the season than earlier, (2) AP voters do not pay attention to the strength of a defeated opponent, and (3) the benefit of winning by a large margin is negligible. I conclude by noting how these results inform debates about a potential playoff in college football.