Revista Matemática Iberoamericana


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Volume 31, Issue 1, 2015, pp. 51–68
DOI: 10.4171/RMI/826

Published online: 2015-03-05

On the product of two $\pi$-decomposable groups

L.S. Kazarin[1], Ana Martínez-Pastor[2] and M. Dolores Pérez-Ramos[3]

(1) Yaroslavl P. Demidov State University, Russian Federation
(2) Universidad Politecnia de Valencia, Spain
(3) Universitat de València, Burjassot (Valencia), Spain

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

Keywords: Finite groups, $\pi$-structure, $\pi$-decomposable groups, products of subgroups, Hall subgroups

Kazarin L.S., Martínez-Pastor Ana, Pérez-Ramos M. Dolores: On the product of two $\pi$-decomposable groups. Rev. Mat. Iberoamericana 31 (2015), 51-68. doi: 10.4171/RMI/826