Abstract
A subgroup H of a finite group G is called \(\mathbb {P}\)-subnormal in G if either \(H = G\) or it is connected to G by a chain of subgroups of prime indices. In this paper, some structural results of finite groups which are factorised as the product of two \(\mathbb {P}\)-subnormal subgroups is showed.
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Alejandre, M.J., Ballester-Bolinches, A., Cossey, J., Pedraza-Aguilera, M.C.: On some permutable products of supersoluble groups. Rev. Mat. Iberoam. 20, 413–425 (2004)
Amberg, B., Franciosi, S., de Giovanni, F.: Products of groups. In: Oxford Mathematical Monographs. The Clarendon Press, New York (1992)
Asaad, M., Shaalan, A.: On the supersolvability of finite groups. Arch. Math. (Basel) 53(4), 318–326 (1989)
Ballester-Bolinches, A., Esteban-Romero, R., Asaad, M.: Products of finite groups. In: de Gruyter Expositions in Mathematics, vol. 53. Walter de Gruyter GmbH & Co. KG, Berlin (2010)
Ballester-Bolinches, A., Ezquerro, L.M.: Classes of finite groups. In: Mathematics and its Applications, vol. 584. Springer, Dordrecht (2006)
Ballester-Bolinches, A., Fakieh, W.M., Pedraza-Aguilera, M.C.: On products of generalised supersoluble finite groups. Mediterr. J. Math., 16(2):46, 7 (2019)
Ballester-Bolinches, A., Pérez-Ramos, M.D.: A question of R. Maier concerning formations. J. Algebra 182(3), 738–747 (1996)
Carocca, A.: On factorized finite groups in which certain subgroups of the factors permute. Arch. Math. (Basel) 71, 257–261 (1998)
Doerk, K., Hawkes, T.: Finite soluble groups. In: De Gruyter Expositions in Mathematics, vol. 4. Walter de Gruyter & Co., Berlin (1992)
Vasil’ev, A.F., Vasil’eva, T.I., Tyutyanov, V.N.: On the finite groups of supersoluble type. Sib. Math. J. 51(6), 1004–1012 (2010)
Vasil’ev, A.F., Vasil’eva, T.I., Tyutyanov, V.N.: On the products of \(\mathbb{{P}}\)-subnormal subgroups of finite groups. Sib. Math. J. 53(1), 47–54 (2012)
Vasil’ev, A.F., Vasil’eva, T.I., Tyutyanov, V.N.: On K-\(\mathbb{{P}}\)-subnormal subgroups of finite groups. Math. Notes 95(3–4), 471–480 (2014)
Vasil’ev, A.F., Vasil’eva, T.I., Tyutyanov, V.N.: Finite widely c-supersoluble groups and their mutually permutable products. Sib. Math. J. 51(3), 476–485 (2016)
Acknowledgements
The first and third authors are supported by the grant PGC2018-095140-B-I00 from the Ministerio de Ciencia, Innovación y Universidades and the Agencia Estatal de Investigación, Spain, and FEDER, European Union and by Prometeo/2017/057 of Generalitat (Valencian Community, Spain). Funding was provided by National Natural Science Foundation of China (Grant no. 11401597).
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Ballester-Bolinches, A., Li, Y., Pedraza-Aguilera, M.C. et al. On Factorised Finite Groups. Mediterr. J. Math. 17, 65 (2020). https://doi.org/10.1007/s00009-020-1500-1
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DOI: https://doi.org/10.1007/s00009-020-1500-1