Free product decompositions in images of certain free products of groups

Let F be the free product of n groups and let R be a normal subgroup generated (as a normal subgroup) by m elements of F, where m &lt; n. The Main Theorem gives sufficient conditions for families of fewer than n−m subgroups in certain quotients of F/R to generate their free product. This leads to a more direct proof of a result of the first author, that if G is a group having a presentation with n generators and m relators, where m &lt; n, then any generating set for G contains n−m elements that freely generate a free subgroup of G. Another consequence is that an n-generator one-relator group cannot be generated by fewer than n−1 subgroups each having a non-trivial abelian normal subgroup.</p

Microbial communities and processes in Arctic permafrost environments

In polar regions, huge layers of frozen ground, termed permafrost, are formed. Permafrost covers more than 25 % of the land surface and significant parts of the coastal sea shelfs. Its habitats are controlled by extreme climate and terrain conditions. Particularly, the seasonal freezing and thawing in the upper active layer of permafrost leads to distinct gradients in temperature and geochemistry. Microorganisms in permafrost environments have to survive extremely cold temperatures, freeze-thaw cycles, desiccation and starvation under long-lasting background radiation over geological time scales. Although the biology of permafrost microorganisms remains relatively unexplored, recent findings show that microbial communities in this extreme environment are composed by members of all three domains of life (Archaea, Bacteria, Eukarya), with a total biomass comparable to temperate soil ecosystems. This chapter describes the environmental conditions of permafrost and reviews recent studies on microbial processes and diversity in permafrost-affected soils as well as the role and significance of microbial communities with respect to global biogeochemical cycles