3 papers
math.GR2025
On the density of Sylow numbers
Andrea Lucchini, Pablo Spiga
Let be a prime number. We say that a positive integer is a Sylow -number if there exists a finite group having exactly Sylow -subgroups. When , every odd int…
math.GR2025
Profinite groups with many elements with large nilpotentizer and generalizations
Martino Garonzi, Andrea Lucchini, Nowras Otmen
Given a profinite group and a family of finite groups closed under taking subgroups, direct products and quotients, denote by the set of elements…
math.GR2025
Commutators between coprime order elements in non-abelian simple groups
Andrea Lucchini, Pablo Spiga
Recent investigations on the set of commutators between the elements of a finite group having relatively prime orders have prompt us to propose a variant of the Ore conjecture: For…