Counting lifts of Brauer characters

In this paper we examine the behavior of lifts of Brauer characters in p-solvable groups where p is an odd prime. In the main result, we show that if \phi \in IBrp(G) is a Brauer character of a solvable group such that \phi has an abelian vertex subgroup Q, then the number of lifts of \phi in Irr(G) is at most |Q|. In order to accomplish this, we develop several results about lifts of Brauer characters in p-solvable groups that were previously only known to be true in the case of groups of odd order.Comment: A different proof of Theorem 1 is in the paper "The number of lifts of Brauer characters with a normal vertex" by J.P. Cossey, M.L.Lewis, and G. Navarro. Hence, we do not expect to try to publish this note. We feel that the proof in this paper is of independent interes

Lifts and vertex pairs in solvable groups

Suppose $G$ is a $p$-solvable group, where $p$ is odd. We explore the connection between lifts of Brauer characters of $G$ and certain local objects in $G$, called vertex pairs. We show that if $\chi$ is a lift, then the vertex pairs of $\chi$ form a single conjugacy class. We use this to prove a sufficient condition for a given pair to be a vertex pair of a lift and to study the behavior of lifts with respect to normal subgroups

Environmental Studies at Newton Lake, Illinois: Tasks 4, 5, and 7

ID: 8658; issued March 1, 1991INHS Technical Report prepared for Marathon Oil Compan

Growth and form of the mound in Gale Crater, Mars: Slope wind enhanced erosion and transport

Ancient sediments provide archives of climate and habitability on Mars. Gale Crater, the landing site for the Mars Science Laboratory (MSL), hosts a 5-km-high sedimentary mound (Mount Sharp/Aeolis Mons). Hypotheses for mound formation include evaporitic, lacustrine, fluviodeltaic, and aeolian processes, but the origin and original extent of Gale’s mound is unknown. Here we show new measurements of sedimentary strata within the mound that indicate ∼3° outward dips oriented radially away from the mound center, inconsistent with the first three hypotheses. Moreover, although mounds are widely considered to be erosional remnants of a once crater-filling unit, we find that the Gale mound’s current form is close to its maximal extent. Instead we propose that the mound’s structure, stratigraphy, and current shape can be explained by growth in place near the center of the crater mediated by wind-topography feedbacks. Our model shows how sediment can initially accrete near the crater center far from crater-wall katabatic winds, until the increasing relief of the resulting mound generates mound-flank slope winds strong enough to erode the mound. The slope wind enhanced erosion and transport (SWEET) hypothesis indicates mound formation dominantly by aeolian deposition with limited organic carbon preservation potential, and a relatively limited role for lacustrine and fluvial activity. Morphodynamic feedbacks between wind and topography are widely applicable to a range of sedimentary and ice mounds across the Martian surface, and possibly other planets

Group elements whose character values are roots of unity

We classify all finite groups $G$ which possesses an element $x\in G$ such that every irreducible character of $G$ takes a root of unity value at $x$

Vertical Atmospheric Structure in a Variable Brown Dwarf: Pressure-dependent Phase Shifts in Simultaneous Hubble Space Telescope-Spitzer Light Curves

Heterogeneous clouds or temperature perturbations in rotating brown dwarfs produce variability in the observed flux. We report time-resolved simultaneous observations of the variable T6.5 brown dwarf 2MASSJ22282889-431026 over the wavelength ranges 1.1-1.7 microns and broadband 4.5 microns. Spectroscopic observations were taken with Wide Field Camera 3 on board the Hubble Space Telescope and photometry with the Spitzer Space Telescope. The object shows sinusoidal infrared variability with a period of 1.4 hr at most wavelengths with peak-to-peak amplitudes between 1.45% and 5.3% of the mean flux. While the light curve shapes are similar at all wavelengths, their phases differ from wavelength to wavelength with a maximum difference of more than half of a rotational period. We compare the spectra with atmospheric models of different cloud prescriptions, from which we determine the pressure levels probed at different wavelengths. We find that the phase lag increases with decreasing pressure level, or higher altitude. We discuss a number of plausible scenarios that could cause this trend of light curve phase with probed pressure level. These observations are the first to probe heterogeneity in an ultracool atmosphere in both horizontal and vertical directions, and thus are an ideal test case for realistic three dimensional simulations of the atmospheric structure with clouds in brown dwarfs and extrasolar planets.Comment: Accepted to ApJL, 6 pages, 3 figures. Minor language updates from v1 to match published versio