On the first Zassenhaus conjecture for integral group rings

It was conjectured by H. Zassenhaus that a torsion unit of an integral group ring of a finite group is conjugate to a group element within the rational group algebra. The object of this note is the computational aspect of a method developed by I.S. Luthar and I.B.S. Passi which sometimes permits an answer to this conjecture. We illustrate the method on certain explicit examples. We prove with additional arguments that the conjecture is valid for any 3-dimensional crystallographic point group. Finally we apply the method to generic character tables and establish a p-variation of the conjecture for the simple groups PSL(2,p)

Group rings of finite simple groups

Let G be a finite non-abelian simple group. In the first part we consider the question whether CG determines G up to isomorphism. This question is closely related to a recent conjecture of B. Huppert that G is determined up to a direct abelian factor by its set of ordinary character degrees. We sketch a proof that a finite simple group is determined by a11 its group algebras over a field

Biological and Statistical Variation in Age Estimation from Pubic Symphyseal Morphology with Regard to Individual Identification and Demographic Profiling

Population variation in the morphological aging process of the pubic symphysis has generated much debate. The question of whether age parameters derived from an American population will reliably estimate age-at-death for East European skeletal populations is important since the ability to accurately estimate an individual’s age-at-death hinges on what standard is used. Consequently, successful age estimation, individual identification, and demographic profiling rests on the ability to correctly define the skeletal parameters of age-at-death. The purpose of this study is to assess the aging process of American and East European populations and to determine what age parameters should be applied to estimate the ages-at-death for unidentified victims. A reference sample of identified individuals with known ages-at-death from Kosovo, Bosnia, and Croatia (n=861) is used to determine the age structure of victims and serves as the informed prior in the Bayesian analysis. Skeletal data comes from a subset of the Balkan reference sample and a comparative American sample. Balkan male (n=212) and female (n=84) pubic symphyses were scored in both the manners of Todd (1920 and 1924) and Suchey-Brooks (Katz and Suchey, 1986; Suchey et al., 1986). Further, repeat observations were completed by four observers for the entire Balkan sample. American male (n=1,560) and female (n=518) pubic symphyses were scored in the manner of Todd (1920 and 1921). The American data were converted from the Todd ten-phase system to the Suchey-Brooks six-phase system, as recommended by Katz and Suchey (1986) for comparative purposes. First, the affect of inter-observer variation on the reliability of estimating age-at-death parameters from the pubic symphyses is investigated. Pearson’s r correlation coefficients among observers for the Todd system are all significant (p \u3c 0.01) and strongly correlate among females. The correlation coefficients among males are more varied and not as strong as the female sample, ranging from r = 0.309 – 0.738. Correlation coefficients among observers for the Suchey-Brooks method are more consistent and higher than those for the Todd method, ranging from r = 0.866 – 0.939 among females and from r = 0.710 – 0.844 among males. Wilcoxon signed ranks tests demonstrate significant differences among observers for both methods. Second, population variation in the aging processes of American and East European populations is tested using proportional odds probit regression. An analysis of deviance is calculated using an improvement chi-square to test the adequacy of the model. No significant association between the aging process of pubic symphyses and population is found (df = 1, chi-square likelihood ratio = 3.209, p = 0.10). However, when males and females are treated separately, there is a significant association among females and the population (df = 1, chi-square likelihood ratio = 15.071, p = 0.001). Finally, a Bayesian statistical analysis is utilized to establish accurate age parameters. The ages-of-transition for each phase are calculated using an unrestrictive cumulative probit model for the Balkan males and the log-age cumulative probit model for the Balkan females. The probability density functions (PDF) for the posterior distributions of age at each symphyseal phase are calculated. The age estimates are based on the calculated age distribution from the Gompertz-Makeham hazard analysis and the ages-of-transition. To estimate the age-at-death for an individual, the highest posterior density regions for each Symphyseal phase is calculated and four different regions are provided (95%, 90%, 75%, and 50%)

Simple classical groups of Lie type are determined by their character degrees

In this paper, we will show that nonabelian simple classical groups of Lie type are uniquely determined by the structure of their complex group algebras.Comment: 10 pages, to appear in Journal of Algebr

Automatic detection of accommodation steps as an indicator of knowledge maturing

Jointly working on shared digital artifacts – such as wikis – is a well-tried method of developing knowledge collectively within a group or organization. Our assumption is that such knowledge maturing is an accommodation process that can be measured by taking the writing process itself into account. This paper describes the development of a tool that detects accommodation automatically with the help of machine learning algorithms. We applied a software framework for task detection to the automatic identification of accommodation processes within a wiki. To set up the learning algorithms and test its performance, we conducted an empirical study, in which participants had to contribute to a wiki and, at the same time, identify their own tasks. Two domain experts evaluated the participants’ micro-tasks with regard to accommodation. We then applied an ontology-based task detection approach that identified accommodation with a rate of 79.12%. The potential use of our tool for measuring knowledge maturing online is discussed