Linking systems are crucial for studying the homotopy theory of fusion systems, but are also of interest from an algebraic point of view. We propose a definition of a linking system associated to a saturated fusion system which is more general than the one currently in the literature and thus allows a more flexible choice of objects of linking systems. More precisely, we define subcentric subgroups of fusion systems in a way that every quasicentric subgroup of a saturated fusion system is subcentric. Whereas the objects of linking systems in the current definition are always quasicentric, the objects of our linking systems only need to be subcentric. We prove that, associated to each saturated fusion system F, there is a unique linking system whose objects are the subcentric subgroups of F. Furthermore, the nerve of such a subcentric linking system is homotopy equivalent to the nerve of the centric linking system associated to F. We believe that the existence of subcentric linking systems opens a new way for a classification of fusion systems of characteristic p-type. The various results we prove about subcentric subgroups give furthermore some evidence that the concept is of interest for studying extensions of linking systems and fusion systems. arXiv:1506.01458v3 [math.GR] 12 Jun 2018 2 E. HENKE

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Natural motion types found in skeletal and muscular systems of vertebrate animals inspire researchers to transfer this ability into engineered motion, which is highly desired in robotic systems. Dielectric elastomer actuators (DEAs) have shown promising capabilities as artificial muscles for driving such structures, as they are soft, lightweight, and can generate large strokes. For maximum performance, dielectric elastomer membranes need to be sufficiently pre-stretched. This fact is challenging, because it is difficult to integrate pre-stretched membranes into entirely soft systems, since the stored strain energy can significantly deform soft elements. Here, we present a soft robotic structure, possessing a bioinspired skeleton integrated into a soft body element, driven by an antagonistic pair of DEA artificial muscles, that enable the robot bending. In its equilibrium state, the setup maintains optimum isotropic pre-stretch. The robot itself has a length of 60 mm and is based on a flexible silicone body, possessing embedded transverse 3D printed struts. These rigid bone-like elements lead to an anisotropic bending stiffness, which only allows bending in one plane while maintaining the DEA's necessary pre-stretch in the other planes. The bones, therefore, define the degrees of freedom and stabilize the system. The DEAs are manufactured by aerosol deposition of a carbon-silicone-composite ink onto a stretchable membrane that is heat cured. Afterwards, the actuators are bonded to the top and bottom of the silicone body. The robotic structure shows large and defined bimorph bending curvature and operates in static as well as dynamic motion. Our experiments describe the influence of membrane pre-stretch and varied stiffness of the silicone body on the static and dynamic bending displacement, resonance frequencies and blocking forces. We also present an analytical model based on the Classical Laminate Theory for the identification of the main influencing parameters. Due to the simple design and processing, our new concept of a bioinspired DEA based robotic structure, with skeletal and muscular reinforcement, offers a wide range of robotic application.

We revisit the notion of a product of a normal subsystem with a p-subgroup as defined by Aschbacher [Asc11, Chapter 8]. In particular, we give a previously unknown, more transparent construction.

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