2-Engel relations between subgroups

In this paper we study groups G generated by two subgroups A and B such that is nilpotent of class at most 2 for all a¿. A and b¿. B. A detailed description of the structure of such groups is obtained, generalizing the classical result of Hopkins and Levi on 2-Engel groups

Products of pairwise totally permutable groups

[EN] In this paper finite groups factorized as products of pairwise totally permutable subgroups are studied in the framework of Fitting classesA.M.-P. and M.D.P.-R. were both supported by Proyecto BMF20001-1667-C03-03, Ministerio de Ciencia y Tecnolog´ıa and FEDER, Spain.Hauck, P.; Martínez Pastor, A.; Pérez-Ramos, M. (2003). Products of pairwise totally permutable groups. Proceedings of the Edinburgh Mathematical Society. 46(1):147-157. https://doi.org/10.1017/S0013091502000299S14715746

Nilpotent-like Fitting formations of finite soluble groups

[EN] In this paper the subnormal subgroup closed saturated formations of finite soluble groups containing nilpotent groups are fully characterised by means of extensions of well-known properties enjoyed by the formation of all nilpotent groups.This research has been supported by Proyecto PB 97-0674-C02-02 of DGICYT, Ministerio de Educación y Ciencia, Spain.Ballester-Bolinches, A.; Pérez-Ramos, M.; Martínez Pastor, A. (2000). Nilpotent-like Fitting formations of finite soluble groups. Bulletin of the Australian Mathematical Society. 62(3):427-433. https://doi.org/10.1017/S0004972700018943S42743362

Products of finite connected subgroups

For a non-empty class of groups L, a finite group G = AB is said to be an L-connected product of the subgroups A and B if e L for all a e A and b e B. In a previous paper, we prove that, for such a product, when L = S is the class of finite soluble groups, then [A, B] is soluble. This generalizes the theorem of Thompson that states the solubility of finite groups whose two-generated subgroups are soluble. In the present paper, our result is applied to extend to finite groups previous research about finite groups in the soluble universe. In particular, we characterize connected products for relevant classes of groups, among others, the class of metanilpotent groups and the class of groups with nilpotent derived subgroup. Additionally, we give local descriptions of relevant subgroups of finite groups

A new LED-LED portable CO2 gas sensor based on an interchangeable membrane system for industrial applications

A new system for CO2 measurement (0-100%) by based on a paired emitter-detector diode arrangement as a colorimetric detection system is described. Two different configurations were tested: configuration 1 (an opposite side configuration) where a secondary inner-filter effect accounts for CO2 sensitivity. This configuration involves the absorption of the phosphorescence emitted from a CO2-insensitive luminophore by an acid-base indicator and configuration 2 wherein the membrane containing the luminophore is removed, simplifying the sensing membrane that now only contains the acid-base indicator. In addition, two different instrumental configurations have been studied, using a paired emitter-detector diode system, consisting of two LEDs wherein one is used as the light source (emitter) and the other is used in reverse bias mode as the light detector. The first configuration uses a green LED as emitter and a red LED as detector, whereas in the second case two identical red LEDs are used as emitter and detector. The system was characterised in terms of sensitivity, dynamic response, reproducibility, stability and temperature influence. We found that configuration 2 presented a better CO2 response in terms of sensitivity

On conditional permutability and saturated formations

Two subgroups A and B of a group G are said to be totally completely conditionally permutable (tcc-permutable) in G if X permutes with Yg for some g ¿ ¿X, Y¿ for all X ¿ A and Y ¿ B. We study the belonging of a finite product of tcc-permutable subgroups to a saturated formation of soluble groups containing all finite supersoluble groups. © 2011 Edinburgh Mathematical Society.This research was supported by Proyectos MTM2007-68010-C03-03 and MTM2010-19938-C03-02, Ministerio de Educacion y Ciencia and FEDER, Spain.Arroyo Jordá, M.; Arroyo Jordá, P.; M.D. Pérez-Ramos (2011). On conditional permutability and saturated formations. Proceedings of the Edinburgh Mathematical Society. 54:309-319. https://doi.org/10.1017/S0013091510000106S30931954Hauck, P., Martínez-Pastor, A., & Pérez-Ramos, M. D. (2003). Injectors and Radicals in Products of Totally Permutable Groups. Communications in Algebra, 31(12), 6135-6147. doi:10.1081/agb-120024871Gállego, M. P., Hauck, P., & Pérez-Ramos, M. D. (2008). On 2-generated subgroups and products of groups. Journal of Group Theory, 11(6). doi:10.1515/jgt.2008.054Carocca, A. (1996). A note on the product of F-subgroups in a finite group. Proceedings of the Edinburgh Mathematical Society, 39(1), 37-42. doi:10.1017/s0013091500022756Asaad, M., & Heliel, A. A. (2003). On permutable subgroups of finite groups. Archiv der Mathematik, 80(2), 113-118. doi:10.1007/s00013-003-0782-4Arroyo-Jordá, M., Arroyo-Jordá, P., Martínez-Pastor, A., & Pérez-Ramos, M. D. (2010). On finite products of groups and supersolubility. Journal of Algebra, 323(10), 2922-2934. doi:10.1016/j.jalgebra.2010.01.001Asaad, M., & Shaalan, A. (1989). On the supersolvability of finite groups. Archiv der Mathematik, 53(4), 318-326. doi:10.1007/bf01195210Beidleman, J., & Heineken, H. (1999). Totally permutable torsion subgroups. Journal of Group Theory, 2(4). doi:10.1515/jgth.1999.027Doerk, K., & Hawkes, T. O. (1992). Finite Soluble Groups. doi:10.1515/9783110870138Huppert, B. (1967). Endliche Gruppen I. Grundlehren der mathematischen Wissenschaften. doi:10.1007/978-3-642-64981-3Hauck, P., Martínez-Pastor, A., & Pérez-Ramos, M. D. (2003). PRODUCTS OF PAIRWISE TOTALLY PERMUTABLE GROUPS. Proceedings of the Edinburgh Mathematical Society, 46(1), 147-157. doi:10.1017/s0013091501000293Ballester-Bolinches, A., Pedraza-Aguilera, M. C., & Pérez-Ramos, M. D. (1996). On finite products of totally permutable groups. Bulletin of the Australian Mathematical Society, 53(3), 441-445. doi:10.1017/s0004972700017196Ballester-Bolinches, A., & Pérez-Ramos, M. D. (1996). A Question of R. Maier Concerning Formations. Journal of Algebra, 182(3), 738-747. doi:10.1006/jabr.1996.0198Hauck, P., Martı́nez-Pastor, A., & Pérez-Ramos, M. D. (2002). Fitting classes and products of totally permutable groups. Journal of Algebra, 252(1), 114-126. doi:10.1016/s0021-8693(02)00012-1Liu, X., Guo, W., & Shum, K. P. (2009). Products of Finite Supersoluble Groups. Algebra Colloquium, 16(02), 333-340. doi:10.1142/s1005386709000327Maier, R. (1992). A Completeness Property of certain Formations. Bulletin of the London Mathematical Society, 24(6), 540-544. doi:10.1112/blms/24.6.540Ballester-Bolinches, A., Pedraza-Aguilera, M. C., & Pérez-Ramos, M. D. (1998). Finite groups which are products of pairwise totally permutable subgroups. Proceedings of the Edinburgh Mathematical Society, 41(3), 567-572. doi:10.1017/s001309150001989

A family of dominant Fitting classes of finite soluble groups

[EN] In this paper a large family of dominant Fitting classes of finite soluble groups and the description of the corresponding injectors are obtained. Classical constructions of nilpotent and Lockett injectors as well as p-nilpotent injectors arise as particular cases.This research has been supported by Proyecto PB 94-0965 of DGICYT, Ministerio de Educacion y Ciencia of Spain.Ballester-Bolinches, A.; Martínez Pastor, A.; Pérez-Ramos, M. (1998). A family of dominant Fitting classes of finite soluble groups. Journal of the Australian Mathematical Society Series a-pure mathematics and statistics. 64(1):33-43. https://doi.org/10.1017/S1446788700001270S3343641[6] Lockett F. P. , On the theory of Fitting classes of finite soluble groups (Ph.D. thesis, University of Warwick, 1971).Ballester-Bolinches, A. (1992). A note on saturated formations. Archiv der Mathematik, 58(2), 110-113. doi:10.1007/bf01191873Ballester-Bolinches, A., Doerk, K., & Pérez-Ramos, M. . (1992). On the lattice of J-subnormal subgroups. Journal of Algebra, 148(1), 42-52. doi:10.1016/0021-8693(92)90235-eDoerk, K., & Hawkes, T. O. (1992). Finite Soluble Groups. doi:10.1515/9783110870138Ballester-Bolinches, A., Pedraza-Aguilera, M. C., & Pérez-Ramos, M. D. (1996). OnF-Subnormal Subgroups andF-Residuals of Finite Soluble Groups. Journal of Algebra, 186(1), 314-322. doi:10.1006/jabr.1996.0375Ballesterbolinches, A., & Perezramos, M. D. (1995). On F-Critical Groups. Journal of Algebra, 174(3), 948-958. doi:10.1006/jabr.1995.116

A reduction theorem for a conjecture on products of two ¿-decomposable groups

[EN] For a set of primes pi, a group X is said to be pi-decomposable if X = X-pi x X-pi' is the direct product of a pi-subgroup X-pi and a pi'-subgroup X-pi', where pi' is the complementary of pi in the set of all prime numbers. The main result of this paper is a reduction theorem for the following conjecture: "Let pi be a set of odd primes. If the finite group G = AB is a product of two pi-decomposable subgroups A = A(pi) x A(pi') and B = B-pi x B-pi', then A(pi)B(pi) = B(pi)A(pi) and this is a Hall pi-subgroup of G." We establish that a minimal counterexample to this conjecture is an almost simple group. The conjecture is then achieved in a forthcoming paper. (C) 2013 Elsevier Inc. All rights reserved.The second and third author have been supported by Proyecto MTM2010-19938-C03-02, Ministerio de Economia y Competitividad, Spain. The first author would like to thank the Universitat de Valencia and the Universitat Politecnica de Valencia for their warm hospitality during the preparation of this paper. He has been also supported by RFBR project 13-01-00469.Kazarin, LS.; Martínez Pastor, A.; Perez Ramos, MD. (2013). A reduction theorem for a conjecture on products of two ¿-decomposable groups. Journal of Algebra. 379:301-313. https://doi.org/10.1016/j.jalgebra.2013.01.017S30131337