One of the most interesting problems in the field Subgroup Lattices of Groups is to find lattice-theoretic characterizations of interesting classes of groups. After explaining this problem by looking at the classical characterizations of cyclic and of finite soluble groups, we first present lattice-theoretic characterizations of some classes of infinite soluble groups. Then for a finite group G we try to determine in its subgroup lattice L(G) the Fitting length of G and properties defined by arithmetical conditions. For this we use some new ideas to determine minimal normal subgroups and the orders of minimal subgroups in L(G).

Introduction

Subarctic and mountain regions are characterized by strong gradients that make their terrestrial and aquatic ecosystems very sensitive to environmental change. The terrestrial Arctic can be delimited by the northern tree line, the 10 °C July isotherm, or the southern extent of discontinuous permafrost which, in the eastern Canadian Arctic for example, currently extends to the southern end of Hudson Bay. In this chapter, we focus on the subarctic region, which, depending on local climates, roughly falls between 50° N and 70° N latitude and includes the transition from boreal forest (taiga) in the south to tundra landscapes in the north, whereas the chapter by Douglas and Smol (this volume) discusses diatom-based studies from the High Arctic. In mountain regions the same steep climatic and environmental gradients are present but over much shorter distances, with the timber line also representing the most prominent ecotone. It is characterized by the transition from closed forest to the most advanced solitary trees (i.e. timber line), to single tree islands (i.e. tree line), and eventually to open, unforested vegetation. This biological boundary can vary in width from tens of meters in mountain regions to many kilometers in the Subarctic. In northern Europe it is formed by deciduous trees such as Betula, Alnus, and Populus, whereas coniferous trees (e.g. Pinus, Picea, Larix, Juniperus) form the tree line in the European Alps, northern North America, and Eurasia.

Introduction

Timber line represents the most prominent ecotone in mountainous and arctic regions. It is characterized by the transition from closed forest to the most advanced solitary trees (i.e., timber line), to single tree islands (i.e., treeline), and eventually to unforested vegetation. This biological boundary can vary in width between tens of meters and many kilometers. In northern Europe it is formed by deciduous trees (Betula, Alnus, Populus), whereas coniferous trees (Pinus, Picea, Larix) form treeline in the Alps, northern North America and Eurasia.

Treeline is primarily related to cold temperatures but a complex set of different climatic factors, as well as the specific adaptation of trees, actually defines the forest limit (e.g., Tranquillini, 1979). This is evident from the decrease in altitude of treeline from subtropical to arctic regions and, on a smaller scale, by the higher forest limit on southern slopes compared to northern slopes (Ellenberg, 1986). In the Alps, timber line represents the transition between the subalpine and the alpine belts (Ozenda, 1985; Ellenberg, 1986). The lower boundary of the alpine belt, however, is difficult to locate as human impact, grazing and climatic oscillations have lowered natural tree limit by several hundred meters in the last millennia (e.g., Lang, 1994; Tinner et al., 1996).

In the north, physical and biotic features are sufficiently distinct to unequivocally separate ‘arctic’ from ‘boreal’ regions. However, great disparity exists among definitions as to where the Boreal region ends and the Arctic region begins (Larsen, 1989).