3 papers
math.GR2026
Finite groups that are the product of every pair of non-conjugate maximal subgroups are soluble
Richie Sater
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-s…
math.GR2026
Generation of finite groups from subgroups of coprime index
Richie Sater
Let denote the least size of a generating set of a finite group . We prove that if has a family of subgroups such that for every $H\in\mathc…
math.GR2026
Finite Soluble Groups Need Not Admit Increasing Unrefinable Subgroup Chains
Richie Sater
In correspondence beginning on August 8, 2026, V. S. Monakhov and I. L. Sokhor communicated the following question to the author: does every finite group have an unrefinable chain…