The nilpotency class of the unit group of a modular group algebra II

LetG be a finitep-group, and letU(G) be the group of units of the group algebraFG, whereF is a field of characteristicp. It is shown that, if the commutative subgroup ofG has order at leastp ², then the nilpotency class ofU(G) is at least 2p−1. The authors are grateful to the Dipartimento di Matematica of the Universita di Trento, and to the Mathematical Institute of the University of Oxford, for their hospitality while this paper was being written. Then are also grateful to Robert Sandling, for communication of results, and problems, prior to publication.     

Low frequency narrow-band calls in bottlenose dolphins (Tursiops truncatus): signal properties, function, and conservation implications

Dolphins routinely use sound for social purposes, foraging and navigating. These sounds are most commonly classified as whistles (tonal, frequency modulated, typical frequencies 5-10 kHz) or clicks (impulsed and mostly ultrasonic). However, some low frequency sounds have been documented in several species of dolphins. Low frequency sounds produced by bottlenose dolphins (Tursiops truncatus) were recorded in three locations along the Gulf of Mexico. Sounds were characterized as being tonal with low peak frequencies (mean?=?990 Hz), short duration (mean?=?0.069 s), highly harmonic, and being produced in trains. Sound duration, peak frequency and number of sounds in trains were not significantly different between Mississippi and the two West Florida sites, however, the time interval between sounds within trains in West Florida was significantly shorter than in Mississippi (t?=?-3.001, p?=?0.011). The sounds were significantly correlated with groups engaging in social activity (F=8.323, p=0.005). The peak frequencies of these sounds were below what is normally thought of as the range of good hearing in bottlenose dolphins, and are likely subject to masking by boat noise.     

Using Berry's phase to detect the Unruh effect at lower accelerations

We show that a detector acquires a Berry phase due to its motion in spacetime. The phase is different in the inertial and accelerated case as a direct consequence of the Unruh effect. We exploit this fact to design a novel method to measure the Unruh effect. Surprisingly, the effect is detectable for accelerations 10(9) times smaller than previous proposals sustained only for times of nanoseconds.     

Metal-Doped Barium Sulphate Nanoparticles Decorated with Gelatin as Antibacterial Agents

Journal of Cluster Science - Nanoparticles are gaining a new impetus in the field of medicine because of their potential to overcome core problems of drug efficacy. Amongst inorganic nanoparticles,...     

The co-degrees of irreducible characters

LetG be a finite group. The co-degree of an irreducible character χ ofG is defined to be the number |G|/χ(1). The set of all prime divisors of all the co-degrees of the nonlinear irreducible characters ofG is denoted by Σ(G). First we show that Σ(G)=π(G) (the set of all prime divisors of |G|) unlessG is nilpotent-by-abelian. Then we make Σ(G) a graph by adjoining two elements of Σ(G) if and only if their product divides a co-degree of some nonlinear character ofG. We show that the graph Σ(G) is connected and has diameter at most 2. Additional information on the graph is given. These results are analogs to theorems obtained for the graph corresponding to the character degrees (by Manz, Staszewski, Willems and Wolf) and for the graph corresponding to the class sizes (by Bertram, Herzog and Mann). Finally, we investigate groups with some restriction on the co-degrees. Among other results we show that ifG has a co-degree which is ap-power for some primep, then the corresponding character is monomial andO _p (G)≠1. Also we describe groups in which each co-degree of a nonlinear character is divisible by at most two primes. These results generalize results of Chillag and Herzog. Other results are proved as well. The paper was written during this author’s visit at the Technion and the University of Tel Aviv. He would like to thank the departments of mathematics at the Technion and the University of Tel Aviv for their hospitality and support.     

Zur Bestimmung des specifischen Gewichtes von Cement

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