611 research outputs found
Wreath products in modular group algebras of some finite 2-groups
Let be field of characteristic 2 and let be a finite non-abelian
2-group with the cyclic derived subgroup , and there exists a central
element of order 2 in . We prove that the unit group of
the group algebra possesses a section isomorphic to the wreath product of
a group of order 2 with the derived subgroup of the group , giving for such
groups a positive answer to the question of A. Shalev.Comment: 3 page
Rewriting the check of 8-rewritability for
The group is called -rewritable for , if for each sequence of
elements there exists a non-identity permutation
such that . Using computers, Blyth and Robinson (1990) verified that
the alternating group is 8-rewritable. We report on an independent
verification of this statement using the computational algebra system GAP, and
compare the performance of our sequential and parallel code with the original
one.Comment: 5 page
Wreath Products in the Unit Group of Modular Group Algebras of 2-groups of Maximal Class
We study the unit group of the modular group algebra KG, where G is a 2-group
of maximal class. We prove that the unit group of KG possesses a section
isomorphic to the wreath product of a group of order two with the commutator
subgroup of the group G.Comment: 12 pages, LaTe
On 2-groups of almost maximal class
Let G be a 2-group of order 2^n, n>5, and nilpotency class n-2. The
invariants of such groups determined by their group algebras over the field of
two elements are given in the paper.Comment: 25 page
The modular isomorphism problem for finite -groups with a cyclic subgroup of index
Let be a prime number, be a finite -group and be a field of
characteristic . The Modular Isomorphism Problem (MIP) asks whether the
group algebra determines the group . Dealing with MIP, we investigated
a question whether the nilpotency class of a finite -group is determined by
its modular group algebra over the field of elements. We give a positive
answer to this question provided one of the following conditions holds: (i)
; (ii) \cl(G)=2; (iii) is cyclic; (iv) is a group of
maximal class and contains an abelian subgroup of index .Comment: 8 page
Hybrid R&D
We develop a model of R&D competition and collaboration in which individual firms carry out independent in-house research and also undertake joint research projects with other firms. We examine the impact of collaboration on in-house research and explore the circumstances under which a hybrid organization of R&D which combines the two is optimal for firms and society. We find that investments in independent research and in joint research are complementary: an increase in the number of joint projects also increases in-house research. Firm profits are highest under a hybrid organization if the number of firms is small (less than 5) while they are highest with pure in-house research if the number of firms is large (5 or more). However, social welfare is maximized under a hybrid organization of R&D in all cases. Our analysis also yields new results on the role of cooperative R&D. We find that non-cooperative decision making by firms leads to larger R&D investments and higher social welfare than fully cooperative decision making. However, a hybrid form of decision making where there is bilateral cooperation in joint projects and non-cooperative decision making in in-house research yields the highest level of welfare in concentrated industries.
Generalized equilibrium in an economy without the survival assumption
It is well known that an equilibrium in the Arrow-Debreu model may
fail to exist if a very restrictive condition called the survival
assumption is not satisfied. We study two approaches that allow
for the relaxation of this condition. Danilov and Sotskov (1990),
and Florig (2001) developed a concept of a generalized equilibrium
based on a notion of hierarchic prices. Marakulin (1990) proposed
a concept of an equilibrium with non-standard prices. In this
paper, we establish the equivalence between non-standard and
hierarchic equilibria. Furthermore, we show that for any specified
system of dividends the set of such equilibria is generically
finite. We also provide a generic characterization of hierarchic
equilibria and give an easy proof of the core equivalence result
Interoperability in the OpenDreamKit Project: The Math-in-the-Middle Approach
OpenDreamKit --- "Open Digital Research Environment Toolkit for the
Advancement of Mathematics" --- is an H2020 EU Research Infrastructure project
that aims at supporting, over the period 2015--2019, the ecosystem of
open-source mathematical software systems. From that, OpenDreamKit will deliver
a flexible toolkit enabling research groups to set up Virtual Research
Environments, customised to meet the varied needs of research projects in pure
mathematics and applications.
An important step in the OpenDreamKit endeavor is to foster the
interoperability between a variety of systems, ranging from computer algebra
systems over mathematical databases to front-ends. This is the mission of the
integration work package (WP6). We report on experiments and future plans with
the \emph{Math-in-the-Middle} approach. This information architecture consists
in a central mathematical ontology that documents the domain and fixes a joint
vocabulary, combined with specifications of the functionalities of the various
systems. Interaction between systems can then be enriched by pivoting off this
information architecture.Comment: 15 pages, 7 figure
The contrasting oceanography of the Rhodes Gyre and the Central Black Sea
The Rhodes Gyre, a prominent feature of the oceanography of the eastern Mediterranean, is modelled as a vertical, continuous flow, cylindrical reactor illuminated during the day at its upper end. If the Gyre is supposed to be in a steady state whilst the concentrations, C, of a chemical are being measured, the nett rate of formation or consumption of the chemical is given by -w d C/d z + u d C/d r, where w is the upward velocity of the water in the vertical, z , direction and u is the velocity of the water in the radial, r, direction. The behaviour of w and u is analysed to show that the Gyre may be used as a field laboratory in which rates of chemical change may be derived from depth profiles together with values of the surface velocities of the Gyre waters. In contrast, the central Black Sea is modelled as an ideal, strongly stratified sea in which the nett rates of formation or consumption of chemicals under steady state conditions are given by Ds d2C/ds 2, where s is the water density and Ds is an eddy diffusion coefficient. Computations reveal that, given better knowledge of its eddy diffusion coefficients, the Black Sea can also be treated as a field laboratory where rates of reaction mediated by bacteria may be derived from depth profiles
On the GruenbergâKegel graph of integral group rings of finite groups
The prime graph question asks whether the GruenbergâKegel graph of an integral group ring â¤G, i.e. the prime graph of the normalized unit group of â¤G, coincides with that one of the group G. In this note, we prove for finite groups G a reduction of the prime graph question to almost simple groups. We apply this reduction to finite groups G whose order is divisible by at most three primes and show that the GruenbergâKegel graph of such groups coincides with the prime graph of G.PostprintPeer reviewe
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