In mathematics, specifically in the field of finite group theory, the Sylow theorems are a collection of theorems that give detailed information about the number of subgroups of fixed order that a ...

The Sylow graph of a finite group originates from recent investigations on certain classes of groups, defined in terms of normalizers of Sylow subgroups. The connectivity of this graph has been proved ...

In this paper, we prove that it is not always true, since we do not have a version of Lagrange’s theorem for generalized digroups. On the other side, we propose and study Sylow-type theorems for ...

The Sylow graph of a finite group originates from recent investigations on certain classes of groups, defined in terms of normalizers of Sylow subgroups. The connectivity of this graph has been proved ...

A project exploring and then extending the implementation of group theory (more specifically Sylow's Theorems) in the functional formal verification language Lean4. In Mathlib, Groups are defined on ...

This course builds on the concepts of groups, rings and fields. A primary focus will be on building tools for classifying certain families of groups, with one highlight being the Sylow Theorems for ...

We show a classification method for finite groupoids and discuss the cardinality of cosets and its relation with the index. We prove a generalization of the Lagrange's Theorem and establish a Sylow ...

Viewing Kan complexes as $\infty$-groupoids implies that pointed and connected Kan complexes are to be viewed as $\infty$-groups. A fundamental question is then: to what extent can one "do group ...