A Sufficient Condition for Nilpotency in a Finite Group

It is shown that finite groups in which the order of the product of every pair of elements of co-prime order is the product of the orders, is nilpotent

Music Composition

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The STAR MAPS-based PiXeL detector

The PiXeL detector (PXL) for the Heavy Flavor Tracker (HFT) of the STAR experiment at RHIC is the first application of the state-of-the-art thin Monolithic Active Pixel Sensors (MAPS) technology in a collider environment. Custom built pixel sensors, their readout electronics and the detector mechanical structure are described in detail. Selected detector design aspects and production steps are presented. The detector operations during the three years of data taking (2014-2016) and the overall performance exceeding the design specifications are discussed in the conclusive sections of this paper

Locally soluble groups with all nontrivial normal subgroups isomorphic

Let $G$ be an infinite, locally soluble group which is isomorphic to all its nontrivial normal subgroups. If $G/G'$ has finite $p$-rank for $p=0$ and for all primes $p$, then $G$ is cyclic

Bicrossed products for finite groups

We investigate one question regarding bicrossed products of finite groups which we believe has the potential of being approachable for other classes of algebraic objects (algebras, Hopf algebras). The problem is to classify the groups that can be written as bicrossed products between groups of fixed isomorphism types. The groups obtained as bicrossed products of two finite cyclic groups, one being of prime order, are described.Comment: Final version: to appear in Algebras and Representation Theor

Extending structures I: the level of groups

Let $H$ be a group and $E$ a set such that $H \subseteq E$. We shall describe and classify up to an isomorphism of groups that stabilizes $H$ the set of all group structures that can be defined on $E$ such that $H$ is a subgroup of $E$. A general product, which we call the unified product, is constructed such that both the crossed product and the bicrossed product of two groups are special cases of it. It is associated to $H$ and to a system $\bigl((S, 1_S,\ast), \triangleleft, \, \triangleright, \, f \bigl)$ called a group extending structure and we denote it by $H \ltimes S$. There exists a group structure on $E$ containing $H$ as a subgroup if and only if there exists an isomorphism of groups $(E, \cdot) \cong H \ltimes S$, for some group extending structure $\bigl((S, 1_S,\ast), \triangleleft, \, \triangleright, \, f \bigl)$. All such group structures on $E$ are classified up to an isomorphism of groups that stabilizes $H$ by a cohomological type set ${\mathcal K}^{2}_{\ltimes} (H, (S, 1_S))$. A Schreier type theorem is proved and an explicit example is given: it classifies up to an isomorphism that stabilizes $H$ all groups that contain $H$ as a subgroup of index 2.Comment: 17 pages; to appear in Algebras and Representation Theor

Presentations: from Kac-Moody groups to profinite and back

We go back and forth between, on the one hand, presentations of arithmetic and Kac-Moody groups and, on the other hand, presentations of profinite groups, deducing along the way new results on both

Simulation of cyclic deformation behavior of selective laser melted and hybrid-manufactured aluminum alloys using the phase-field method

Selective laser melting process has already been developed for many metallic materials, including steel, aluminum, and titanium. The quasistatic properties of these materials have been found to be comparable or even better than their conventionally-manufactured counterparts; however, for their reliable applications in operational components, their fatigue behavior plays a critical role, which is dominated by several process-related features, like surface roughness, remnant porosity, microstructure, and residual stresses, which are controlled by the processing features, like imparted energy density to the material, its corresponding solidification behavior, the cooling rate in the process, as well as post-processing treatments. This study investigates the influence of these parameters on the cyclic deformation behavior of selective laser melted as well as hybrid-manufactured aluminum alloys. The corresponding microstructural features and porosity conditions are evaluated for developing correlations between the process conditions to microstructure, the deformation behavior, and the corresponding fatigue lives. From the numerical point of view, damage development with respect to process-induced cyclic deformation behavior is assessed by the phase-field method, which has been identified as an appropriate method for the determination of fatigue life at the respective applied stress levels. Fatigue strength of SLM-processed parts is found better than their cast counterparts, while hybridization has further increased fatigue strength. No effect of test frequency on the fatigue life could be established

Residual properties of the modular group and other free products

AbstractUsing a probabilistic approach we establish new residual properties of the modular group PSL2(Z), and of more general free products. We prove that the modular group is residually in any infinite collection of finite simple groups not containing a Suzuki group Sz(q) or a 4-dimensional symplectic group PSp4(q) with q a power of 2 or 3. This result is best possible, since the groups excluded are not quotients of the modular group. We also show that if S is a collection of classical groups of unbounded rank, then an arbitrary free product A∗B of nontrivial finite groups, not both 2-groups, is residually S, and prove results about free products A∗Z