Skip to main content
Log in

The Fitting length of a product of mutually permutable finite groups

  • Published:
Acta Mathematica Hungarica Aims and scope Submit manuscript

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 \({\ell_{p}(G) \leq {\rm max} \{\ell_{p}(G_{i}) \mid i = 1, 2, \ldots, r\}+1}\).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. Ballester-Bolinches, R. Esteban-Romero and M. Asaad, Products of Finite Groups, Walter de Gruyter (Berlin, 2010).

  2. 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)

    Article  MathSciNet  MATH  Google Scholar 

  3. Doerk K., Hawkes T.: Finite Soluble Groups. Walter de Gruyter, Berlin (1992)

    Book  MATH  Google Scholar 

  4. Robinson D.J.S.: A Course in the Theory of Groups, 2nd ed. Springer-Verlag, New York (1996)

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to E. Jabara.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Jabara, E. The Fitting length of a product of mutually permutable finite groups. Acta Math. Hungar. 159, 206–210 (2019). https://doi.org/10.1007/s10474-019-00923-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10474-019-00923-8

Key words and phrases

Mathematics Subject Classification

Navigation