Author

Richie Sater

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Preprint Aug 2026

Finite groups that are the product of every pair of non-conjugate maximal subgroups are soluble

We prove that every finite group that is the product of every pair of its non-conjugate maximal subgroups is soluble, answering Problem 10.34 of the Kourovka Notebook. The almost-simple case was proved by Tikhonenko and Tyutyanov. We treat the remaining minimal-counterexample branch, where the unique minimal normal sub...

Richie Sater · 0 citations

Preprint Aug 2026

Generation of finite groups from subgroups of coprime index

Let $d(G)$ denote the least size of a generating set of a finite group $G$. We prove that if $G$ has a family $\mathcal H$ of subgroups such that $d(H)\leq d$ for every $H\in\mathcal H$ and $\gcd\{\lvert G:H\rvert:H\in\mathcal H\}=1$, then $d(G)\leq d+1$. This gives an affirmative answer to Kourovka Problem 21.87. The...

Richie Sater · 0 citations