Abstract
The aim of this paper is to obtain a bound for the \(p\)-length of a \(p\)-soluble group \(G\) whose elements of order \(p\) or order \(4\) (if \(p = 2\)) of a Sylow \(p\)-subgroup of a residual subgroup of \(G\) are contained in the \(k\)-th term of the upper central series of a Sylow \(p\)-subgroup of \(G\).
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References
Ballester-Bolinches, A., Esteban-Romero, R., Asaad, M.: Products of finite groups. In: De Gruyter Expositions in Mathematics, vol. 53. Walter de Gruyter, Berlin (2010). doi:10.1515/9783110220612
Ballester-Bolinches, A., Esteban-Romero, R., Ezquerro, L.M.: On the \(p\)-length of some finite \(p\)-soluble groups. Israel J. Math. 204, 359–371 (2014). doi:10.1007/s11856-014-1095-y
Ballester-Bolinches, A., Ezquerro, L.M.: Classes of Finite Groups. In: Mathematics and its Applications, vol. 584. Springer, New York (2006)
Ballester-Bolinches, A., Pedraza-Aguilera, M.C.: On minimal subgroups of finite groups. Acta Math. Hungar. 73(4), 335–342 (1996). doi:10.1007/BF00052909
Bryukhanova, E.G.: The \(2\)-length and \(2\)-period of a finite solvable group. Algebra Logic 18(1), 5–20 (1979). doi:10.1007/BF01669309
Doerk, K., Hawkes, T.: Finite Soluble Groups. In: De Gruyter Expositions in Mathematics, vol. 4. Walter de Gruyter, Berlin, New York (1992). doi:10.1515/9783110870138
Hall, P., Higman, G.: On the \(p\)-length of \(p\)-soluble groups and reduction theorems for Burnside’s problem. Proc. London Math. Soc. III Ser. 6, 1–42 (1956). doi:10.1112/plms/s3-6.1.1
Khukhro, E.I.: On \(p\)-soluble groups with a generalized \(p\)-central or powerful Sylow \(p\)-subgroup. Int. J. Group Theory 1(2), 51–57 (2012)
Acknowledgments
The first author has been supported by the grant MTM2010-19938-C01-01 from the Ministerio de Ciencia e Innovación of Spain, by the grant MTM2014-54707-C3-1-P from the Ministerio de Economía y Competitividad of Spain and by a project of the National Natural Science Foundation of China (11271085).
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Ballester-Bolinches, A., Ezquerro, L.M. & Su, N. On bounds for the \(p\)-length of finite \(p\)-soluble groups. Collect. Math. 67, 373–378 (2016). https://doi.org/10.1007/s13348-015-0144-0
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DOI: https://doi.org/10.1007/s13348-015-0144-0