Open Access
2009 On the product of two $\pi$-decomposable soluble groups
L. S. Kazarin, A. Martínez-Pastor, M. D. Pérez-Ramos
Publ. Mat. 53(2): 439-456 (2009).


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.


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L. S. Kazarin. A. Martínez-Pastor. M. D. Pérez-Ramos. "On the product of two $\pi$-decomposable soluble groups." Publ. Mat. 53 (2) 439 - 456, 2009.


Published: 2009
First available in Project Euclid: 20 July 2009

zbMATH: 1200.20016
MathSciNet: MR2543859

Primary: 20D20 , 20D40

Keywords: $\pi$-decomposable groups , Hall subgroups , Products of groups

Rights: Copyright © 2009 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.53 • No. 2 • 2009
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