Group classes and mutually permutable products

AbstractLet G=AB be the mutually permutable product of the nontrivial subgroups A and B of the group G. Then A or B contains a nontrivial normal subgroup of G. It is also established that S(G)∩A=S(A), where S(U) is the solvable radical of U. These facts lead to some generalized results about mutually permutable products of SC-groups. It is also shown that if G is a PTS-group, then A and B are PST-groups

On the Intersection of Certain Maximal Subgroups of a Finite Group

Let Δ(G) denote the intersection of all non-normal maximal subgroups of a group G. We introduce the class of T2-groups which are defined as the groups G for which G/Δ(G) is a T-group, that is, a group in which normality is a transitive relation. Several results concerning the class T2 are discussed. In particular, if G is a solvable group, then Sylow permutability is a transitive relation in G if and only if every subgroup H of G is a T2-group such that the nilpotent residual of H is a Hall subgroup of H

On finite pp-groups whose automorphisms are all central

An automorphism $\alpha$ of a group $G$ is said to be central if $\alpha$ commutes with every inner automorphism of $G$. We construct a family of non-special finite $p$-groups having abelian automorphism groups. These groups provide counter examples to a conjecture of A. Mahalanobis [Israel J. Math., {\bf 165} (2008), 161 - 187]. We also construct a family of finite $p$-groups having non-abelian automorphism groups and all automorphisms central. This solves a problem of I. Malinowska [Advances in group theory, Aracne Editrice, Rome 2002, 111-127].Comment: 11 pages, Counter examples to a conjecture from [Israel J. Math., {\bf 165} (2008), 161 - 187]; This paper will appear in Israel J. Math. in 201

Orthonasal and retronasal detection thresholds of 26 aroma compounds in a model alcohol-free beer: effect of threshold calculation method

Detection thresholds are used routinely to determine the odour-active compounds in foods. The composition of a food matrix, such as hydrophobicity or solids content, has an impact on the release of flavour compounds, and thus on thresholds. In the case of beer, thresholds determined in alcoholic beer may not be the same for alcohol-free beer (AFB). Therefore, the aim of this study was to determine detection thresholds for aroma compounds typically found in beer within a model AFB. The model was designed to match the sugar concentration and pH of an AFB brewed by a cold contact process. Thresholds were measured using a 3-AFC procedure and calculated using either Best Estimate Threshold (BET) method or by logistic regression. Moreover, an algorithm for the removal of false positives was applied to adjust the assessors’ raw responses. Retronasal thresholds were generally lower than orthonasal. Those calculated by BET were significantly higher (p < 0.05) than those from logistic regression, and removal of false positives also produced significantly higher thresholds than those from raw data. The use of logistic regression has the advantage of providing the mathematical model describing the behaviour of the group. The results from this study can be used to better understand the role of flavour compounds in AFB and the effect of the calculation method to prevent under- or overestimated results

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

Functional regulation of FEN1 nuclease and its link to cancer

Flap endonuclease-1 (FEN1) is a member of the Rad2 structure-specific nuclease family. FEN1 possesses FEN, 5′-exonuclease and gap-endonuclease activities. The multiple nuclease activities of FEN1 allow it to participate in numerous DNA metabolic pathways, including Okazaki fragment maturation, stalled replication fork rescue, telomere maintenance, long-patch base excision repair and apoptotic DNA fragmentation. Here, we summarize the distinct roles of the different nuclease activities of FEN1 in these pathways. Recent biochemical and genetic studies indicate that FEN1 interacts with more than 30 proteins and undergoes post-translational modifications. We discuss how FEN1 is regulated via these mechanisms. Moreover, FEN1 interacts with five distinct groups of DNA metabolic proteins, allowing the nuclease to be recruited to a specific DNA metabolic complex, such as the DNA replication machinery for RNA primer removal or the DNA degradosome for apoptotic DNA fragmentation. Some FEN1 interaction partners also stimulate FEN1 nuclease activities to further ensure efficient action in processing of different DNA structures. Post-translational modifications, on the other hand, may be critical to regulate protein–protein interactions and cellular localizations of FEN1. Lastly, we also review the biological significance of FEN1 as a tumor suppressor, with an emphasis on studies of human mutations and mouse models

The wonders of flap endonucleases: structure, function, mechanism and regulation.

Processing of Okazaki fragments to complete lagging strand DNA synthesis requires coordination among several proteins. RNA primers and DNA synthesised by DNA polymerase α are displaced by DNA polymerase δ to create bifurcated nucleic acid structures known as 5'-flaps. These 5'-flaps are removed by Flap Endonuclease 1 (FEN), a structure-specific nuclease whose divalent metal ion-dependent phosphodiesterase activity cleaves 5'-flaps with exquisite specificity. FENs are paradigms for the 5' nuclease superfamily, whose members perform a wide variety of roles in nucleic acid metabolism using a similar nuclease core domain that displays common biochemical properties and structural features. A detailed review of FEN structure is undertaken to show how DNA substrate recognition occurs and how FEN achieves cleavage at a single phosphate diester. A proposed double nucleotide unpairing trap (DoNUT) is discussed with regards to FEN and has relevance to the wider 5' nuclease superfamily. The homotrimeric proliferating cell nuclear antigen protein (PCNA) coordinates the actions of DNA polymerase, FEN and DNA ligase by facilitating the hand-off intermediates between each protein during Okazaki fragment maturation to maximise through-put and minimise consequences of intermediates being released into the wider cellular environment. FEN has numerous partner proteins that modulate and control its action during DNA replication and is also controlled by several post-translational modification events, all acting in concert to maintain precise and appropriate cleavage of Okazaki fragment intermediates during DNA replication