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Silvia Onofrei

Publications and source records attributed to Silvia Onofrei.

11 recordsLinked to original sources
arXiv2011

Saturated fusion systems with parabolic families

Let G be group; a finite p-subgroup S of G is a Sylow p-subgroup if every finite p-subgroup of G is conjugate to a subgroup of S. In this paper, we examine the relations between the fusion system over S which is given by conjugation in G and a certain chamber system C, on which G acts chamber transitively with chamber stabilizer N_G(S). Next, we introduce the notion of a fusion system with a parabolic family and we show that a chamber system can be associated to such a fusion system. We determine some conditions the chamber system has to fulfill in order to assure the saturation of the underlying fusion system. We give an application to fusion systems with parabolic families of classical type.

math.GR↗
arXiv2011

On the vertices of indecomposable summands of certain Lefschetz modules

We study the reduced Lefschetz module of the complex of p-radical and p-centric subgroups. We assume that the underlying group G has parabolic characteristic p and the centralizer of a certain noncentral p-element has a component with central quotient H a finite group of Lie type in characteristic p. A non-projective indecomposable summand of the associated Lefschetz module lies in a non-principal block of G and it is a Green correspondent of an inflated, extended Steinberg module for a Lie subgroup of H. The vertex of this summand is the defect group of the block in which it lies.

math.GR↗
arXiv2008

A characteristic subgroup for fusion systems

As a counterpart for the prime 2 to Glauberman's $ZJ$-theorem, Stellmacher proves that any nontrivial 2-group $S$ has a nontrivial characteristic subgroup $W(S)$ with the following property. For any finite $Σ_4$-free group $G$, with $S$ a Sylow 2-subgroup of $G$ and with $O_2(G)$ self-centralizing, the subgroup $W(S)$ is normal in $G$. We generalize Stellmacher's result to fusion systems. A similar construction of $W(S)$ can be done for odd primes and gives rise to a Glauberman functor.

math.RT↗
arXiv2008

On fixed point sets and Lefschetz modules for sporadic simple groups

We consider 2-local geometries and other subgroup complexes for sporadic simple groups. For six groups, the fixed point set of a noncentral involution is shown to be equivariantly homotopy equivalent to a standard geometry for the component of the centralizer. For odd primes, fixed point sets are computed for sporadic groups having an extraspecial Sylow p-subgroup of order p^3, acting on the complex of those p-radical subgroups containing a p-central element in their centers. Vertices for summands of the associated reduced Lefschetz modules are described.

math.GR↗
arXiv2007

On a space related to the affine building of type E7

A locally truncated geometry with diagram of type affine E7 is studied. One considers a parapolar space, locally of type A_{7,4}, which is subject to an extra axiom. A covering of this space is constructed; it is proved that this covering space is a rank 6, residually connected, locally truncated diagram geometry which is a homomorphic image of a truncated building of affine type E7. Consequently, the initial parapolar space is also a homomorphic image of a truncated building.

math.GR↗
arXiv2007

A characterization of two classes of locally truncated diagram geometries

We study locally truncated geometries that are parapolar spaces locally of type A_{n-1,j}(K) with n>6 and j=3,4. Residually connected sheaves over these geometries are constructed. It is proved that these geometries are residually connected diagram geometries whose universal 2-covers are truncations of buildings.

math.GR↗
arXiv2003

Solar System test for the existence of gravitational waves

Starting from a static spherically symmetric solution of the Einstein's field equations in the second approximation in the perfect fluid scheme, in the exterior of the source, the corresponding metrics depend on a dimensionless parameter $α$ . Taking the Sun for the source, the influence of $α$ on the classical Solar System tests of the general relativity is estimated, the only $α$-dependent one being the Shapiro radar-echo delay experiment. Performing such a test in given conditions within a precision better than $10^{-2}$, it is possible to obtain an experimental value for $α$ . If $α=1$, the Einstein's equations in the weak field approximation take the D'Alembert form, which attests the existence of gravitational waves

gr-qc↗