We compute the Bieri-Neumann-Strebel invariants Σ1 for generalized solvable Baumslag-Solitar groups Γn and their finite index subgroups. Using Σ1, we show that certain subgroups of cannot be isomorphic to Γk any k. In addition, use BNS-invariants give a new proof property R∞

In this survey paper the authors specify all known findings related to norms of a~group and their generalizations (since 2016 in more details). Special attention is paid analysis own study different generalized norms, particularly norm non-cyclic subgroups, Abelian decomposable subgroups relations between them.

The use of generalized additive models in statistical data analysis suffers from the restriction to few explanatory variables and the problems of selection of smoothing parameters. Generalized additive model boosting circumvents these problems by means of stagewise fitting of weak learners. A fitting procedure is derived which works for all simple exponential family distributions, including bin...

A nilpotent group G is a finite group that is the direct product of its Sylow p-subgroups. Theorem 1.1 (Fitting's Theorem) Let G be a finite group, and let H and K be two nilpotent normal subgroups of G. Then HK is nilpotent. Hence in any finite group there is a unique maximal normal nilpotent subgroup, and every nilpotent normal subgroup lies inside this; it is called the Fitting subgroup, and...

This short course covers the application of the statistical theory of extreme values to climate, in general, and to climate change, in particular. The statistical theory of extreme values is briefly reviewed, both the extremal types theorem with its application via the block maxima approach (i.e., fitting the generalized extreme value distribution) and the point process model with its applicati...

The generalised Fitting subgroup of a finite group is the group generated by all subnormal subgroups that are either nilpotent or quasisimple. The importance of this subgroup in finite group theory stems from the fact that it always contains its own centraliser, so that any finite group is an abelian extension of a group of automorphisms of its generalised Fitting subgroup. We define a class of...