A subset X of a finite group G is said to be prime-power-independent if each element in has prime power order and there no proper Y with 〈Y,Φ(G)〉=〈X,Φ(G)〉, where Φ(G) the Frattini subgroup G. Bpp all generating sets for have same cardinality. We prove that, Bpp, then solvable. Pivoting on some recent results Krempa Stocka (2014); (2020), this yields complete classification Bpp-groups.

The recursive computation of the interlace polynomial introduced by Arratia, Bollobás and Sorkin is defined in terms of a new pivoting operation on undirected simple graphs. In this paper, we interpret the new pivoting operation on graphs in terms of standard pivoting (on matrices). Specifically, we show that, up to swapping vertex labels, Arratia et al.’s pivoting operation on a graph is equiv...

Abstract Tram manufacturers have different ways of approaching the design low-floor trams with compact and reliable running gears, therefore several tram architectures can still be found. A complete standardization is nearly impossible, technical innovations more easily introduced if compared to conventional railway vehicles, but trend towards large-scale based on vehicle “platforms” seen in re...

We propose several techniques as alternatives to partial pivoting to stabilize sparse Gaussian elimination. From numerical experiments we demonstrate that for a wide range of problems the new method is as stable as partial pivoting. The main advantage of the new method over partial pivoting is that it permits a priori determination of data structures and communication pattern, which makes it mo...

Abstract This chapter considers the LU factorization of a general nonsymmetric nonsingular sparse matrix A . In practice, numerical pivoting for stability and/or ordering to limit fill-in in factors is often needed and computed then permuted PAQ Pivoting discussed Chapter 7 algorithms 8

Complex symmetric systems do not in general admit a Cholesky factorization without pivoting, as would be the case for hermitian systems. Nevertheless, for some complex symmetric systems, as those coming from the discretization of boundary integral formulations, pivoting can be avoided. We present a Cholesky factorization algorithm for such complex symmetric systems. We propose a LAPACK-style im...

In this short paper we prove that the classic simplex method with the mostnegative-reduced-cost pivoting rule (Dantzig 1947) for solving the Markov decision problem (MDP) with a fixed discount rate is a strongly polynomial-time algorithm. The result seems surprising since this very pivoting rule was shown to be exponential for solving a general linear programming (LP) problem, and the simplex (...