67 research outputs found

    Finitely presented wreath products and double coset decompositions

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    We characterize which permutational wreath products W^(X)\rtimes G are finitely presented. This occurs if and only if G and W are finitely presented, G acts on X with finitely generated stabilizers, and with finitely many orbits on the cartesian square X^2. On the one hand, this extends a result of G. Baumslag about standard wreath products; on the other hand, this provides nontrivial examples of finitely presented groups. For instance, we obtain two quasi-isometric finitely presented groups, one of which is torsion-free and the other has an infinite torsion subgroup. Motivated by the characterization above, we discuss the following question: which finitely generated groups can have a finitely generated subgroup with finitely many double cosets? The discussion involves properties related to the structure of maximal subgroups, and to the profinite topology.Comment: 21 pages; no figure. To appear in Geom. Dedicat

    Aryl urea substituted fatty acids: a new class of protonophoric mitochondrial uncoupler that utilises a synthetic anion transporter

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    A new mitochondrial uncoupler that forms membrane permeable dimers through interactions of remote acidic and anion receptor groups.</p

    Torsion-free groups in which every subgroup is subnormal

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    Aryl urea substituted fatty acids: A new class of protonophoric mitochondrial uncoupler that utilises a synthetic anion transporter

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    Respiring mitochondria establish a proton gradient across the mitochondrial inner membrane (MIM) that is used to generate ATP. Protein-independent mitochondrial uncouplers collapse the proton gradient and disrupt ATP production by shuttling protons back across the MIM in a protonophoric cycle. Continued cycling relies on the formation of MIM-permeable anionic species that can return to the intermembrane space after deprotonation in the mitochondrial matrix. Previously described protonophores contain acidic groups that are part of delocalised p-systems that provide large surfaces for charge delocalisation and facilitate anion permeation across the MIM. Here we present a new class of protonophoric uncoupler based on aryl-urea substituted fatty acids in which an acidic group and a p-system are separated by a long alkyl chain. The aryl-urea group in these molecules acts as a synthetic anion receptor that forms intermolecular hydrogen bonds with the fatty acid carboxylate after deprotonation. Dispersal of the negative charge across the aryl-urea system produces lipophilic dimeric complexes that can permeate the MIM and facilitate repeated cycling. Substitution of the aryl-urea group with lipophilic electron withdrawing groups is critical to complex lipophilicity and uncoupling activity. The aryl-urea substituted fatty acids represent the first biological example of mitochondrial uncoupling mediated by the interaction of a fatty acid and an anion receptor moiety, via self-assembly.This study was supported by grants from the Australian National Health and Medical Research Council (1031686 and 1087248). PAG thanks the Australian Research Council (DP200100453 and DP180100612) for funding
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