The $D_π$-property on products of $π$-decomposable groups

L. S. Kazarin, A. Martínez-Pastor, M. D. Pérez-Ramos

英文摘要：

The aim of this paper is to prove the following result: Let $π$ be a set of odd primes. If the group $G=AB$ is the product of two $π$-decomposable subgroups $A=A_π\times A_{π'}$ and $B=B_π\times B_{π'}$, then $G$ has a unique conjugacy class of Hall $π$-subgroups, and any $π$-subgroup is contained in a Hall $π$-subgroup (i.e. $G$ satisfies property $D_π$).

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