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Acta Mathematica Hungarica

, Volume 159, Issue 1, pp 206–210 | Cite as

The Fitting length of a product of mutually permutable finite groups

  • E. JabaraEmail author
Article
  • 31 Downloads

Abstract

Let the finite soluble group \({G = G_{1}G_{2} \cdots G_{r}}\) be the product of pairwise mutually permutable subgroups \({G_{1}, G_{2}, \ldots, G_{r}}\), let h(G) and \({\ell_{p}(G)}\) be respectively the Fitting length and the p-length of G. The aim of this paper is to prove that \({h(G) \leq {\rm max} \{h(G_{i}) \mid i = 1, 2, \ldots, r\}+1}\) and \({\ell_{p}(G) \leq {\rm max} \{\ell_{p}(G_{i}) \mid i = 1, 2, \ldots, r\}+1}\).

Key words and phrases

mutually permutable product Fitting length p-length 

Mathematics Subject Classification

primary 20D40 secondary 20D10 20F17 

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References

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    A. Ballester-Bolinches, R. Esteban-Romero and M. Asaad, Products of Finite Groups, Walter de Gruyter (Berlin, 2010).Google Scholar
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    Cossey J., Li Y.: On the p-length of the mutually permutable product of two p-soluble groups. Arch. Math. (Basel) 110, 533–537 (2018)MathSciNetCrossRefzbMATHGoogle Scholar
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    Doerk K., Hawkes T.: Finite Soluble Groups. Walter de Gruyter, Berlin (1992)CrossRefzbMATHGoogle Scholar
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    Robinson D.J.S.: A Course in the Theory of Groups, 2nd ed. Springer-Verlag, New York (1996)CrossRefGoogle Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2019

Authors and Affiliations

  1. 1.DFBC – Università di VeneziaVeneziaItaly

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