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

On sigma-subnormality criteria in finite sigma-soluble groups

[EN] Let sigma = {sigma(i) : i is an element of I} be a partition of the set P of all prime numbers. A subgroup X of a finite group G is called sigma-subnormal in G if there is a chain of subgroups X = X-0 subset of X-1 subset of center dot center dot center dot subset of X-n = G where for every j = 1,..., n the subgroup X j-1 is normal in X j or X j /CoreX j ( X j-1) is a si -group for some i. I. In the special case that s is the partition of P into sets containing exactly one prime each, the sigma-subnormality reduces to the familiar case of subnormality. In this paper some sigma-subnormality criteria for subgroups of s-soluble groups, or groups in which every chief factor is a sigma(i)-group, for some sigma(i) sigma s, are showed.The first and third authors are supported by the grant PGC2018-095140-B-I00 from the Ministerio de Ciencia, Innovacion y Universidades and the Agencia Estatal de Investigacion, Spain, and FEDER, European Union and Prometeo/2017/057 of Generalitat (Valencian Community, Spain). The second author was supported by the State Program of Science Researchers of the Republic of Belarus (Grant 19-54 "Convergence-2020").Ballester-Bolinches, A.; Kamornikov, SF.; Pedraza Aguilera, MC.; Pérez-Calabuig, V. (2020). On sigma-subnormality criteria in finite sigma-soluble groups. Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas. 114(2):1-9. https://doi.org/10.1007/s13398-020-00824-4S191142Amberg, B., Franciosi, S., De Giovanni, F.: Products of Groups. Oxford Mathematical Monographs. Clarendon Press, Oxford (1992)Ballester-Bolinches, A., Ezquerro, L.M.: Classes of Finite Groups, Vol. 584 of Mathematics and its Applications. Springer, New York (2006)Ballester-Bolinches, A., Kamornikov, S.F., Pedraza-Aguilera, M.C., Yi, X.: On -subnormal subgroups of factorised finite groups (Preprint)Casolo, C.: Subnormality in factorizable finite soluble groups. Arch. Math. 57, 12–13 (1991)Doerk, K., Hawkes, T.: Finite Soluble Groups. Walter De Gruyter, Berlin (1992)Fumagalli, Francesco: On subnormality criteria for subgroups in finite groups. J. Lond. Math. Soc. 76(2), 237–252 (2007)Kamornikov, S.F., Shemetkova, O.L.: On $${{\cal{F}}}$$-subnormal subgroups of a finite factorised group. Probl. Phys. Math. Tech. 1, 61–63 (2018)Khukhro, E.I., Mazurov, V.D.: Unsolved Problems in Group Theory. The Kourovka notebook. Institut Matematiki SO RAN, Novosibirsk, No. 19 (2018)Lennox, J.C., Stonehewer, S.E.: Subnormal Subgroups of Groups. Clarendon Press, Oxford (1987)Maier, R.: Um problema da teoria dos subgrupos subnormais. Bol. Soc. Bras. Mat. 8(2), 127–130 (1977)Maier, R., Sidki, R.: A note on subnormality in factorizable finite groups. Arch. Math. 42, 97–101 (1984)Skiba, A.N.: A generalization of a Hall theorem. J. Algebra Appl. 15(4), 13 (2016)Skiba, A.N.: On $$\sigma$$-subnormal and $$\sigma$$-permutable subgroups of finite groups. J. Algebra 436, 1–16 (2015)Skiba, A.N.: On -properties of finite groups I. Probl. Phys. Math. Tech. 4, 89–96 (2014)Skiba, A.N.: On -properties of finite groups II. Probl. Phys. Math. Tech. 3(24), 70–83 (2015)Skiba, A.N.: On some arithmetic properties of finite groups. Note Mat. 36, 65–89 (2016)Wielandt, H.: Subnormalität in faktorisierten endlichen Grupppen. J. Algebra 69, 305–311 (1981

Fiber Coupled Transceiver with 6.5 THz Bandwidth for Terahertz Time-Domain Spectroscopy in Reflection Geometry

We present a fiber coupled transceiver head for terahertz (THz) time-domain reflection measurements. The monolithically integrated transceiver chip is based on iron (Fe) doped In0.53Ga0.47As (InGaAs:Fe) grown by molecular beam epitaxy. Due to its ultrashort electron lifetime and high mobility, InGaAs:Fe is very well suited as both THz emitter and receiver. A record THz bandwidth of 6.5 THz and a peak dynamic range of up to 75 dB are achieved. In addition, we present THz imaging in reflection geometry with a spatial resolution as good as 130 µm. Hence, this THz transceiver is a promising device for industrial THz sensing applications

Prefactorized subgroups in pairwise mutually permutable products

The final publication is available at Springer via http://dx.doi.org/10.1007/s10231-012-0257-yWe continue here our study of pairwise mutually and pairwise totally permutable products. We are looking for subgroups of the product in which the given factorization induces a factorization of the subgroup. In the case of soluble groups, it is shown that a prefactorized Carter subgroup and a prefactorized system normalizer exist.Aless stringent property have F-residual, F-projector and F-normalizer for any saturated formation F including the supersoluble groups.The first and fourth authors have been supported by the grant MTM2010-19938-C03-01 from MICINN (Spain).Ballester-Bolinches, A.; Beidleman, J.; Heineken, H.; Pedraza Aguilera, MC. (2013). Prefactorized subgroups in pairwise mutually permutable products. Annali di Matematica Pura ed Applicata. 192(6):1043-1057. https://doi.org/10.1007/s10231-012-0257-yS104310571926Amberg B., Franciosi S., de Giovanni F.: Products of Groups. Clarendon Press, Oxford (1992)Ballester-Bolinches, A., Pedraza-Aguilera, M.C., Pérez-Ramos, M.D.: Totally and Mutually Permutable Products of Finite Groups, Groups St. Andrews 1997 in Bath I. London Math. Soc. Lecture Note Ser. 260, 65–68. Cambridge University Press, Cambridge (1999)Ballester-Bolinches A., Pedraza-Aguilera M.C., Pérez-Ramos M.D.: On finite products of totally permutable groups. Bull. Aust. Math. Soc. 53, 441–445 (1996)Ballester-Bolinches A., Pedraza-Aguilera M.C., Pérez-Ramos M.D.: Finite groups which are products of pairwise totally permutable subgroups. Proc. Edinb. Math. Soc. 41, 567–572 (1998)Ballester-Bolinches A., Beidleman J.C., Heineken H., Pedraza-Aguilera M.C.: On pairwise mutually permutable products. Forum Math. 21, 1081–1090 (2009)Ballester-Bolinches A., Beidleman J.C., Heineken H., Pedraza-Aguilera M.C.: Local classes and pairwise mutually permutable products of finite groups. Documenta Math. 15, 255–265 (2010)Beidleman J.C., Heineken H.: Mutually permutable subgroups and group classes. Arch. Math. 85, 18–30 (2005)Beidleman J.C., Heineken H.: Group classes and mutually permutable products. J. Algebra 297, 409–416 (2006)Carocca A.: p-supersolvability of factorized groups. Hokkaido Math. J. 21, 395–403 (1992)Carocca, A., Maier, R.: Theorems of Kegel-Wielandt Type Groups St. Andrews 1997 in Bath I. London Math. Soc. Lecture Note Ser. 260, 195–201. Cambridge University Press, Cambridge, (1999)Doerk K., Hawkes T.: Finite Soluble Groups. Walter De Gruyter, Berlin (1992)Maier R., Schmid P.: The embedding of quasinormal subgroups in finite groups. Math. Z. 131, 269–272 (1973

Schreier type theorems for bicrossed products

We prove that the bicrossed product of two groups is a quotient of the pushout of two semidirect products. A matched pair of groups $(H, G, \alpha, \beta)$ is deformed using a combinatorial datum $(\sigma, v, r)$ consisting of an automorphism $\sigma$ of $H$, a permutation $v$ of the set $G$ and a transition map $r: G\to H$ in order to obtain a new matched pair $\bigl(H, (G,*), \alpha', \beta' \bigl)$ such that there exist an $\sigma$-invariant isomorphism of groups $H {}_{\alpha} \bowtie_{\beta} G \cong H {}_{\alpha'} \bowtie_{\beta'} (G,*)$. Moreover, if we fix the group $H$ and the automorphism \sigma \in \Aut(H) then any $\sigma$-invariant isomorphism $H {}_{\alpha} \bowtie_{\beta} G \cong H {}_{\alpha'} \bowtie_{\beta'} G'$ between two arbitrary bicrossed product of groups is obtained in a unique way by the above deformation method. As applications two Schreier type classification theorems for bicrossed product of groups are given.Comment: 21 pages, final version to appear in Central European J. Mat

Novel Interactions between Actin and the Proteasome Revealed by Complex Haploinsufficiency

Saccharomyces cerevisiae has been a powerful model for uncovering the landscape of binary gene interactions through whole-genome screening. Complex heterozygous interactions are potentially important to human genetic disease as loss-of-function alleles are common in human genomes. We have been using complex haploinsufficiency (CHI) screening with the actin gene to identify genes related to actin function and as a model to determine the prevalence of CHI interactions in eukaryotic genomes. Previous CHI screening between actin and null alleles for non-essential genes uncovered ∼240 deleterious CHI interactions. In this report, we have extended CHI screening to null alleles for essential genes by mating a query strain to sporulations of heterozygous knock-out strains. Using an act1Δ query, knock-outs of 60 essential genes were found to be CHI with actin. Enriched in this collection were functional categories found in the previous screen against non-essential genes, including genes involved in cytoskeleton function and chaperone complexes that fold actin and tubulin. Novel to this screen was the identification of genes for components of the TFIID transcription complex and for the proteasome. We investigated a potential role for the proteasome in regulating the actin cytoskeleton and found that the proteasome physically associates with actin filaments in vitro and that some conditional mutations in proteasome genes have gross defects in actin organization. Whole-genome screening with actin as a query has confirmed that CHI interactions are important phenotypic drivers. Furthermore, CHI screening is another genetic tool to uncover novel functional connections. Here we report a previously unappreciated role for the proteasome in affecting actin organization and function

Roles for H2A.Z and Its Acetylation in GAL1 Transcription and Gene Induction, but Not GAL1-Transcriptional Memory

H2A.Z does not appear to have a role in GAL1 transcriptional memory, but it does have both acetylation-dependent and acetylation-independent roles in GAL1 induction and expression

Roles of Trm9- and ALKBH8-like proteins in the formation of modified wobble uridines in Arabidopsis tRNA

Uridine at the wobble position of tRNA is usually modified, and modification is required for accurate and efficient protein translation. In eukaryotes, wobble uridines are modified into 5-methoxycarbonylmethyluridine (mcm5U), 5-carbamoylmethyluridine (ncm5U) or derivatives thereof. Here, we demonstrate, both by in vitro and in vivo studies, that the Arabidopsis thaliana methyltransferase AT1G31600, denoted by us AtTRM9, is responsible for the final step in mcm5U formation, thus representing a functional homologue of the Saccharomyces cerevisiae Trm9 protein. We also show that the enzymatic activity of AtTRM9 depends on either one of two closely related proteins, AtTRM112a and AtTRM112b. Moreover, we demonstrate that AT1G36310, denoted AtALKBH8, is required for hydroxylation of mcm5U to (S)-mchm5U in tRNAGlyUCC, and has a function similar to the mammalian dioxygenase ALKBH8. Interestingly, atalkbh8 mutant plants displayed strongly increased levels of mcm5U, and also of mcm5Um, its 2′-O-ribose methylated derivative. This suggests that accumulated mcm5U is prone to further ribose methylation by a non-specialized mechanism, and may challenge the notion that the existence of mcm5U- and mcm5Um-containing forms of the selenocysteine-specific tRNASec in mammals reflects an important regulatory process. The present study reveals a role in for several hitherto uncharacterized Arabidopsis proteins in the formation of modified wobble uridines