Hall-like theorems in products of $\pi$-decomposable groups

Abstract: We discuss in this talk some Hall-like results for a finite group $G=AB$ which is the product of two $\pi$-decomposable subgroups $A = A_{\pi}\times A_{\pi'}$ and $B=B_\pi\times B_{\pi'}$, being $\pi$ a set of odd primes. More concretely, we show that such a group $G$ has a unique conjugacy class of Hall $\pi$-subgroups, and any $\pi$-subgroup is contained in a Hall $\pi$-subgroup (i.e. $G$ satisfies property $D_\pi$).

(Joint work with Lev S. Kazarin and M. Dolores Pérez-Ramos.)

group theory

Audience: researchers in the topic

Finite Groups in Valencia

Series comments: The seminar meets weekly from February 26th to March 30th 2021.

For a detailed schedule and registration details, please visit the seminar webpage at

sites.google.com/view/finite-groups-seminar2021