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 \({\ell_{p}(G) \leq {\rm max} \{\ell_{p}(G_{i}) \mid i = 1, 2, \ldots, r\}+1}\).
Similar content being viewed by others
References
A. Ballester-Bolinches, R. Esteban-Romero and M. Asaad, Products of Finite Groups, Walter de Gruyter (Berlin, 2010).
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)
Doerk K., Hawkes T.: Finite Soluble Groups. Walter de Gruyter, Berlin (1992)
Robinson D.J.S.: A Course in the Theory of Groups, 2nd ed. Springer-Verlag, New York (1996)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
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
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10474-019-00923-8