2,605 research outputs found
Kimmerle conjecture for the Held and O'Nan sporadic simple groups
Using the Luthar--Passi method, we investigate the Zassenhaus and Kimmerle
conjectures for normalized unit groups of integral group rings of the Held and
O'Nan sporadic simple groups. We confirm the Kimmerle conjecture for the Held
simple group and also derive for both groups some extra information relevant to
the classical Zassenhaus conjecture.Comment: 9 page
Torsion units in integral group rings of Janko simple groups
Using the Luthar--Passi method, we investigate the classical Zassenhaus
conjecture for the normalized unit group of integral group rings of Janko
sporadic simple groups. As a consequence, we obtain that the Gruenberg-Kegel
graph of the Janko groups , and is the same as that of the
normalized unit group of their respective integral group ring.Comment: 23 pages, to appear in Math.Comp
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
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