## Publicacions Matemàtiques

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

#### Abstract

Let the group $G=AB$ be a product of two $\pi$-decomposable subgroups $A=O_\pi(A) \times O_{\pi'}(A)$ and $B=O_\pi(B) \times O_{\pi'}(B)$ where $\pi$ is a set of primes. The authors conjecture that $O_\pi(A)O_\pi(B)=O_\pi(B)O_\pi(A)$ if $\pi$ is a set of odd primes. In this paper it is proved that the conjecture is true if $A$ and $B$ are soluble. A similar result with certain additional restrictions holds in the case $2 \in \pi$. Moreover, it is shown that the conjecture holds if $O_{\pi'}(A)$ and $O_{\pi'}(B)$ have coprime orders.

#### Article information

Source
Publ. Mat., Volume 53, Number 2 (2009), 439-456.

Dates
First available in Project Euclid: 20 July 2009

https://projecteuclid.org/euclid.pm/1248095663

Mathematical Reviews number (MathSciNet)
MR2543859

Zentralblatt MATH identifier
1200.20016

#### Citation

Kazarin, L. S.; Martínez-Pastor, A.; Pérez-Ramos, M. D. On the product of two $\pi$-decomposable soluble groups. Publ. Mat. 53 (2009), no. 2, 439--456. https://projecteuclid.org/euclid.pm/1248095663

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