Pretibial myxoedema: a case report with scanning electron microscopy.

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Prime power indices in factorised groups

[EN] Let the group G = AB be the product of the subgroups A and B. We determine some structural properties of G when the p-elements in A. B have prime power indices in G, for some prime p. More generally, we also consider the case that all prime power order elements in A. B have prime power indices in G. In particular, when G = A = B, we obtain as a consequence some known results.The first author is supported by Proyecto Prometeo II/2015/011, Generalitat Valenciana (Spain), and the second author is supported by Proyecto MTM2014-54707-C3-1-P, Ministerio de Economia, Industria y Competitividad (Spain). The results in this paper are part of the third author's Ph.D. thesis, and he acknowledges the predoctoral grant ACIF/2016/170, Generalitat Valenciana (Spain).Felipe Román, MJ.; Martínez-Pastor, A.; Ortiz-Sotomayor, VM. (2017). Prime power indices in factorised groups. Mediterranean Journal of Mathematics. 14(6):1-15. https://doi.org/10.1007/s00009-017-1023-6S115146Amberg, B., Franciosi, S., de Giovanni, F.: Products of Groups. Oxford University Press Inc., New York (1992)Baer, R.: Group elements of prime power index. Trans. Am. Math. Soc. 75, 20–47 (1953)Ballester-Bolinches, A., Cossey, J., Li, Y.: Mutually permutable products and conjugacy classes. Monatsh. Math. 170, 305–310 (2013)Ballester-Bolinches, A., Esteban-Romero, R., Asaad, M.: Products of finite groups, vol. 53 of de Gruyter Expositions in Mathematics, Berlin (2010)Berkovich, Y., Kazarin, L.S.: Indices of elements and normal structure of finite groups. J. Algebra 283, 564–583 (2005)Camina, A.R., Camina, R.D.: Implications of conjugacy class size. J. Group Theory 1(3), 257–269 (1998)Camina, A.R., Shumyatsky, P., Sica, C.: On elements of prime-power index in finite groups. J. Algebra 323, 522–525 (2010)Chillag, D., Herzog, M.: On the length of the conjugacy classes of finite groups. J. Algebra 131, 110–125 (1990)Doerk, K., Hawkes, T.: Finite Soluble Groups, vol. 4 of de Gruyter Expositions in Mathematics, Berlin (1992)Felipe, M.J., Martínez-Pastor, A., Ortiz-Sotomayor, V.M.: On finite groups with square-free conjugacy class sizes. Int. J. Group Theory (to appear)Kurzweil, H., Stellmacher, B.: The theory of finite groups: an introduction. Springer, New York (2004)Liu, X., Wang, Y., Wei, H.: Notes on the length of conjugacy classes of finite groups. J. Pure Appl. Algebra 196, 111–117 (2005

A Concerted Kinase Interplay Identifies PPARγ as a Molecular Target of Ghrelin Signaling in Macrophages

The peroxisome proliferator-activator receptor PPARγ plays an essential role in vascular biology, modulating macrophage function and atherosclerosis progression. Recently, we have described the beneficial effect of combined activation of the ghrelin/GHS-R1a receptor and the scavenger receptor CD36 to induce macrophage cholesterol release through transcriptional activation of PPARγ. Although the interplay between CD36 and PPARγ in atherogenesis is well recognized, the contribution of the ghrelin receptor to regulate PPARγ remains unknown. Here, we demonstrate that ghrelin triggers PPARγ activation through a concerted signaling cascade involving Erk1/2 and Akt kinases, resulting in enhanced expression of downstream effectors LXRα and ABC sterol transporters in human macrophages. These effects were associated with enhanced PPARγ phosphorylation independently of the inhibitory conserved serine-84. Src tyrosine kinase Fyn was identified as being recruited to GHS-R1a in response to ghrelin, but failure of activated Fyn to enhance PPARγ Ser-84 specific phosphorylation relied on the concomitant recruitment of docking protein Dok-1, which prevented optimal activation of the Erk1/2 pathway. Also, substitution of Ser-84 preserved the ghrelin-induced PPARγ activity and responsiveness to Src inhibition, supporting a mechanism independent of Ser-84 in PPARγ response to ghrelin. Consistent with this, we found that ghrelin promoted the PI3-K/Akt pathway in a Gαq-dependent manner, resulting in Akt recruitment to PPARγ, enhanced PPARγ phosphorylation and activation independently of Ser-84, and increased expression of LXRα and ABCA1/G1. Collectively, these results illustrate a complex interplay involving Fyn/Dok-1/Erk and Gαq/PI3-K/Akt pathways to transduce in a concerted manner responsiveness of PPARγ to ghrelin in macrophages

Implications of Conjugacy Class Size

this paper we prove another special case, but this time approaching the question from the opposite direction

Conjugacy classes of maximal cyclic subgroups and nilpotence class of pp-groups

http://dx.doi.org/10.1017/S000497271200033

Finite line-transitive linear spaces: parameters and normal point-partitions

Until the 1990's the only known finite linear spaces admitting line-transitive, pointimprimitive groups of automorphisms were Desarguesian projective planes and two linear spaces with 91 points and line size 6. In 1992 a new family of 467 such spaces was constructed, all having 729 points and line size 8. These were shown to be the only linear spaces attaining an upper bound of Delandtsheer and Doyen on the number of points. Projective planes, and the linear spaces just mentioned on 91 or 729 points, are the only known examples of such spaces, and in all cases the line-transitive group has a non-trivial normal subgroup intransitive on points. The orbits of this normal subgroup form a partition of the point set called a normal point-partition. We give a systematic analysis of finite line-transitive linear spaces with normal point-partitions. As well as the usual parameters of linear spaces there are extra parameters connected with the normal point-partition that affect the structure of the linear space. Using this analysis we characterise the line-transitive linear spaces for which the values of various of these parameters are small. In particular we obtain a classification of all imprimitive linetransitive linear spaces that ‘nearly attain’ the Delandtsheer-Doyen upper bound. © 2003, by Walter de Gruyter GmbH & Co. KG. All rights reserved.(Math.Reviews 2004k :20002)SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Transitive projective planes

A long-standing conjecture is that any transitive finite projective plane is Desarguesian. We make a contribution towards a proof of this conjecture by showing that a group acting transitively on the points of a non-Desarguesian projective plane must not contain any components.Peer Reviewe