JournalsrmiVol. 31, No. 1pp. 51–68

On the product of two π\pi-decomposable groups

  • L.S. Kazarin

    Yaroslavl P. Demidov State University, Russian Federation
  • Ana Martínez-Pastor

    Universidad Politecnia de Valencia, Spain
  • M. Dolores Pérez-Ramos

    Universitat de València, Burjassot (Valencia), Spain
On the product of two $\pi$-decomposable groups cover
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Abstract

The aim of this paper is to prove the following result: let π\pi be a set of odd primes. If the finite group G=ABG=AB is a product of two π\pi-decomposable subgroups A=Oπ(A)×Oπ(A)A=\mathrm O_{\pi}(A) \times \mathrm O_{\pi'}(A) and B=Oπ(B)×Oπ(B)B=\mathrm O_{\pi}(B) \times \mathrm O_{\pi'}(B), then Oπ(A)Oπ(B)=Oπ(B)Oπ(A)\mathrm O_\pi(A)\mathrm O_\pi(B)=\mathrm O_\pi(B)\mathrm O_\pi(A) and this is a Hall π\pi-subgroup of GG.

Cite this article

L.S. Kazarin, Ana Martínez-Pastor, M. Dolores Pérez-Ramos, On the product of two π\pi-decomposable groups. Rev. Mat. Iberoam. 31 (2015), no. 1, pp. 51–68

DOI 10.4171/RMI/826