Fitting height and lengths of laws in finite solvable groups

Let G be a finite solvable group, and let h(G) denote its Fitting height, namely the length of a shortest normal series in G with nilpotent factors. We show, that any law in G has length at least h(G). This result is then used to improve a previously given bound on the nonsolvable length of finite nonsolvable groups

Ice-ocean interactions at Riiser-Larsen Ice Shelf assessed by unveiling of seabed beneath it

The Riiser-Larsen ice shelf is the fourth largest ice shelf on Earth. The detailed depth and shape of the seabed beneath the ice shelf is entirely unknown. Since bed topography beneath ice shelves generally poses the controlling factor of heat exchange between the open ocean and water cavities, this unknown factor inhibits proper assessment of ice-ocean interactions. In coastal Dronning Maud Land, the intrusion of Warm Deep Water – a warm intermediate water mass transported by the Weddell Gyre – into the ice shelf cavities is strongly dependent on seabed depth. We are addressing this shortcoming by generating a bathymetric model beneath the ice shelf based on the inversion of gravity data and complementary data sets of magnetic and ice penetrating radar data, all acquired during the joint AWI-BGR airborne campaign ‘RIISERBATHY’ in 2022/23. The resulting model will have a resolution of 5 to 10 km and is complemented offshore by shipborne hydroacoustic data. We present the first versions of the model here. Modelled depths can be compared to thermocline depths of available in-situ oceanographic data close to and at the calving fronts. In doing so, we will identify key regions of possible entry for Warm Deep Water into the cavity beneath the ice shelf