Distributive Gruppen endlicher Ordnung [Finite Distributive Groups]

TL;DR

This paper introduces the concept of distributive groups, explores their properties, structure, and generation methods, and presents related theorems including an index theorem, with additional appendices.

Contribution

It defines distributive groups, investigates their properties and structure, and establishes foundational theorems including an index theorem for these groups.

Findings

Distributive groups can be generated from associative and distributive groups.

Properties and structure of distributive groups are characterized.

An index theorem for distributive groups is established.

Abstract

This is a translation. I have added translations for (possibly) outdated definitions in an appendix at the end. In this paper, we define distributive groups and show some properties of them. We then concern ourselves with the homogeinity of distributive groups, before showing how they can be generated from both associative and distributive groups. After that, we look at subgroups and define an index theorem for distributive groups before describing the structure of distributive groups. Finally, we present two addenda with several theorems that we proved while trying to prove that $\left|(A.p).(A.q)\right|=\left|A\right|$.