283,963 research outputs found
Endotrivial Modules for the General Linear Group in a Nondefining Characteristic
Suppose that is a finite group such that , and that is a central subgroup of .
Let be the abelian group of equivalence classes of endotrivial
-modules, where is an algebraically closed field of
characteristic~ not dividing . We show that the torsion free rank of
is at most one, and we determine in the case that the Sylow
-subgroup of is abelian and nontrivial. The proofs for the torsion
subgroup of use the theory of Young modules for
and a new method due to Balmer for computing the
kernel of restrictions in the group of endotrivial modules
Mild pro-p-groups with 4 generators
Let p be an odd prime and S a finite set of primes = 1 mod p. We give an
effective criterion for determining when the Galois group G=G_S(p) of the
maximal p-extension of Q unramified outside of S is mild when |S|=4 and the cup
product H^1(G,Z/pZ) \otimes H^1(G,Z/pZ) --> H^2(G,Z/pZ) is surjective.Comment: 12 pages. No figures. LaTe
Liouville Vortex And Kink Solutions Of The Seiberg--Witten Equations
The Seiberg--Witten equations, when dimensionally reduced to \bf R^{2}\mit,
naturally yield the Liouville equation, whose solutions are parametrized by an
arbitrary analytic function . The magnetic flux is the integral of
a singular Kaehler form involving ; for an appropriate choice of ,
coaxial or separated vortex configurations with are
obtained when the integral is regularized. The regularized connection in the
\bf R^{1}\mit case coincides with the kink solution of theory.Comment: 14 pages, Late
On the degree of MIMO systems
MIMO channels and wireless communications
systems have generated a great deal of renewed
interest in linear system theory. This paper presents two
results. The first is a simple proof based on first principles,
of the known fact that the McMillan degree of a causal
M×M MIMO system is at least as large as the degree of
its determinant. The second is a new result which shows
that the degree of the M×M system z^(−1) G(z) is equal
to the degree of G(z) plus M if and only if the causal
system G(z) has an anticausal inverse
Packing Chromatic Number of Distance Graphs
The packing chromatic number of a graph is the smallest
integer such that vertices of can be partitioned into disjoint classes
where vertices in have pairwise distance greater than
. We study the packing chromatic number of infinite distance graphs , i.e. graphs with the set of integers as vertex set and in which two
distinct vertices are adjacent if and only if . In
this paper we focus on distance graphs with . We improve some
results of Togni who initiated the study. It is shown that for sufficiently large odd and
for sufficiently large even . We also give a lower bound 12 for
and tighten several gaps for with small .Comment: 13 pages, 3 figure
- …