598,187 research outputs found
Finite p-groups with central automorphism group of minimal order
We study finite p-groups G of coclass upto 4 for which the group Aut_z(G) of
all central automorphisms of G is of minimal possible order. As a consequence,
we obtain very short and elementary proofs of main results of Sharma and Gumber
[7].Comment: 4 page
Signalizers in groups of Lie type
We classify all CG(t)-signalizers, where G is a finite group of Lie type and t is an automorphism
of G of prime order s > 3. Our results extend existing work by Korchagina ([Ko], [Ko2])
Riemannian geometry of quantum groups and finite groups with nonuniversal differentials
We construct noncommutative `Riemannian manifold' structures on dual
quasitriangular Hopf algebras such as with its standard bicovariant
differential calculus, using the quantum frame bundle formalism introduced
previously. The metric is provided by the braided-Killing form on the
braided-Lie algebra on the tangent space and the -bein by the Maurer-Cartan
form. We also apply the theory to finite sets and in particular to finite group
function algebras with differential calculi and Killing forms determined
by a conjugacy class. The case of the permutation group is worked out
in full detail and a unique torsion free and cotorsion free or `Levi-Civita'
connection is obtained with noncommutative Ricci curvature essentially
proportional to the metric (an Einstein space). We also construct Dirac
operators in the metric background, including on finite groups such as .
In the process we clarify the construction of connections from gauge fields
with nonuniversal calculi on quantum principal bundles of tensor product form.Comment: 43 pages, 1 figure. Revised August 2001 to cut page length (eg
deleted appendix) for publication in CMP. Also fleshed out ex. of q-Killing
metric for q-SU_2 previously mentioned (no significant additions
Cooperation in the Prisoner's Dilemma Game Based on the Second-Best Decision
In the research addressing the prisoner's dilemma game, the effectiveness and accountableness of the method allowing for the emergence of cooperation is generally discussed. The most well-known solutions for this question are memory based iteration, the tag used to distinguish between defector and cooperator, the spatial structure of the game and the either direct or indirect reciprocity. We have also challenged to approach the topic from a different point of view namely that temperate acquisitiveness in decision making could be possible to achieve cooperation. It was already shown in our previous research that the exclusion of the best decision had a remarkable effect on the emergence of an almost cooperative state. In this paper, we advance the decision of our former research to become more explainable by introducing the second-best decision. If that decision is adopted, players also reach an extremely high level cooperative state in the prisoner's dilemma game and also in that of extended strategy expression. The cooperation of this extended game is facilitated only if the product of two parameters is under the criticality. In addition, the applicability of our model to the problem in the real world is discussed.Cooperation, Altruism, Agent-Based Simulation, Evolutionary Game Theory
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