Transitive simple subgroups of wreath products in product action

A transitive simple subgroup of a finite symmetric group is very rarely contained in a full wreath product in product action. All such simple permutation groups are determined in this paper. This remarkable conclusion is reached after a definition and detailed examination of `Cartesian decompositions' of the permuted set, relating them to certain `Cartesian systemsof subgroups'. These concepts, and the bijective connections between them, are explored in greater generality, with specific future applications in mind.Comment: Submitte

History As Retrospective Anthropology

History As Retrospective Anthropolog

FRANK NORRIS: THE NATURALIST AS VICTORIAN

FRANK NORRIS: THE NATURALIST AS VICTORIA

Stage-specific histone modification profiles reveal global transitions in the Xenopus embryonic epigenome.

Vertebrate embryos are derived from a transitory pool of pluripotent cells. By the process of embryonic induction, these precursor cells are assigned to specific fates and differentiation programs. Histone post-translational modifications are thought to play a key role in the establishment and maintenance of stable gene expression patterns underlying these processes. While on gene level histone modifications are known to change during differentiation, very little is known about the quantitative fluctuations in bulk histone modifications during development. To investigate this issue we analysed histones isolated from four different developmental stages of Xenopus laevis by mass spectrometry. In toto, we quantified 59 modification states on core histones H3 and H4 from blastula to tadpole stages. During this developmental period, we observed in general an increase in the unmodified states, and a shift from histone modifications associated with transcriptional activity to transcriptionally repressive histone marks. We also compared these naturally occurring patterns with the histone modifications of murine ES cells, detecting large differences in the methylation patterns of histone H3 lysines 27 and 36 between pluripotent ES cells and pluripotent cells from Xenopus blastulae. By combining all detected modification transitions we could cluster their patterns according to their embryonic origin, defining specific histone modification profiles (HMPs) for each developmental stage. To our knowledge, this data set represents the first compendium of covalent histone modifications and their quantitative flux during normogenesis in a vertebrate model organism. The HMPs indicate a stepwise maturation of the embryonic epigenome, which may be causal to the progressing restriction of cellular potency during development