Annals of Mathematics
In our ﬁrst article  we developed a new view of Gauss composition of binary quadratic forms which led to several new laws of composition on various other spaces of forms. Moreover, we showed that the groups arising from these composition laws were closely related to the class groups of orders in quadratic number ﬁelds, while the spaces underlying those composition laws were closely related to certain exceptional Lie groups.
Abstract. Thes are the notes for the first part ofMath 594, University ofMichigan,Winter
1994, exactly as they were handed out during the course except for some minor corrections.
Please send comments and corrections to me at firstname.lastname@example.org using “Math594” as
Project Gutenberg’s Theory of Groups of Finite Order, by William Burnside This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at www.gutenberg.org
Title: Theory of Groups of Finite Order Author: William Burnside Release Date: August 2, 2012
Let N be a nilpotent group normal in a group G. Suppose that G acts transitively
upon the points of a nite non-Desarguesian projective plane P. We prove that, if
P has square order, then N must act semi-regularly on P.
In addition we prove that if a nite non-Desarguesian projective plane P admits
more than one nilpotent group which is regular on the points of P then P has
non-square order and the automorphism group of P has odd order.
We prove that the sequence of projective quantum SU(n) representations of the mapping class group of a closed oriented surface, obtained from the projective ﬂat SU(n)-Verlinde bundles over Teichm¨ller space, is asymptotically u faithful. That is, the intersection over all levels of the kernels of these representations is trivial, whenever the genus is at least 3. For the genus 2 case, this intersection is exactly the order 2 subgroup, generated by the hyper-elliptic involution, in the case of even degree and n = 2. Otherwise the intersection is also trivial in the genus 2 case. ...
This stability provided reassurance that we could calculate an average rate for each age cohort
from across the five AHS periods (i.e., 1995, 1997, 1999, 2001, and 2003). We then applied
these calculated rates to the Census population projections. The result is a reasonable set of
projections for the number of householders, within each age group, through 2030.
One of our research goals was to extend this to projections of tenure status (i.e., owning vs.
renting) for each age group. In order to do this, we used a method similar to that used to
In a classic paper, Gerstenhaber showed that ﬁrst order deformations of an associative k-algebra a are controlled by the second Hochschild cohomology group of a. More generally, any n-parameter ﬁrst order deformation of a gives, due to commutativity of the cup-product on Hochschild cohomology, a graded algebra morphism Sym• (kn ) → Ext2•bimod (a, a).
This work is concerned with such matters as: (1) the review and analysis of proposals
submitted by industry groups; (2) attending public hearings and meetings with the public
and industry groups; (3) conducting referenda; (4) establishing machinery for operation
of agreements and orders; (5) preparing reports recommending administrative and
regulatory action, and appropriate documents to achieve such action; (6) giving market
administrators advice and assistance regarding the interpretation of orders and
agreements, and administrative and procedural matters; (7) interpret...
Since it has been shown that car-sharing can contribute markedly to reducing the
burden of automobile traffic on the environment, the Swedish National Road
Administration considers it important that the establishment and growth of car-
sharing schemes be enouraged. There is a need of clarifying, however, just what
car-sharing is and what quality requirements should be met by car-sharing
groups in order for public benefits and support to be provided them.
Because it is sometimes hard for investors to become experts
on various businesses—for example, what are the best steel,
automobile, or telephone companies—investors often depend
on professionals who are trained to investigate companies and
recommend companies that are likely to succeed. Since it takes
work to pick the stocks or bonds of the companies that have
the best chance to do well in the future, many investors choose
to invest in mutual funds.
In summarization, sentence ordering is conducted to enhance summary readability by accommodating text coherence. We propose a grouping-based ordering framework that integrates local and global coherence concerns. Summary sentences are grouped before ordering is applied on two levels: group-level and sentence-level. Different algorithms for grouping and ordering are discussed. The preliminary results on single-document news datasets demonstrate the advantage of our method over a widely accepted method. ...
Just putting a group of people together in the same room or online space does not guarantee that they will work together effectively or that they will achieve the results they desire. In order to be effective, groups need to have a shared sense of purpose and motivation to achieving this purpose, whatever the reason that brings them together.
This paper studies the responses of residential property and equity prices,
inflation and economic activity to monetary policy shocks in 17 countries,
using data spanning 1986-2006. We estimate VARs for individual economies
and panel VARs in which we distinguish between groups of countries on the
basis of the characteristics of their financial systems. The results suggest that
using monetary policy to offset asset price movements in order to guard
against financial instability may have large effects on economic activity.
three groups of 40 perch breeders were reared in order to study the effects of 3 different levels of dietary n-3 and n-6 fatty acids on egg quality. two experimental diets, r1 and r2 (n-3/n-6 = 0.13 and 35.54, respectively), were compared to one commercial food, r3 (n-3/n-6 = 3.48). spawning and fertilization rates were high for diets r1 and r3, which displayed a n-3/n-6 ratio of 0.77 and 2.34 in the eggs, respectively, by comparison with r2 (n-3/n-6 = 4.87), which produced low reproductive performances. We can conclude that dietary n-3 and n-6 FA levels influence egg and larval...
The reporting entity concept was adopted by the
accounting profession in June 1992 in an attempt to
reduce the reporting requirements imposed on
certain entities by the application of Accounting
Standards. Under this concept, “reporting entities”
are required to prepare a financial report in
compliance with all Accounting Standards and
Urgent Issues Group Consensus Views (referred to
as general purpose financial reports (GPFRs)).
Two centuries ago, in his celebrated work Disquisitiones Arithmeticae of 1801, Gauss laid down the beautiful law of composition of integral binary quadratic forms which would play such a critical role in number theory in the decades to follow. Even today, two centuries later, this law of composition still remains one of the primary tools for understanding and computing with the class groups of quadratic orders. It is hence only natural to ask whether higher analogues of this composition law exist that could shed light on the structure of other algebraic number rings and ﬁelds. ...
Weyl group multiple Dirichlet series were associated with a root system Φ and a number ﬁeld F containing the n-th roots of unity by Brubaker, Bump, Chinta, Friedberg and Hoﬀstein  and Brubaker, Bump and Friedberg  provided n is suﬃciently large; their coeﬃcients involve n-th order Gauss sums. The case where n is small is harder, and is addressed in this paper when Φ = Ar . “Twisted” Dirichet series are considered, which contain the series of  as a special case.