# The Herzog-Sch\"onheim conjecture for solvable groups

## TL;DR

This paper investigates the Herzog-Schönheim conjecture within solvable groups, aiming to determine whether partitions into cosets necessarily include two with identical indices, thus contributing to understanding the structure of such partitions.

## Contribution

The paper provides new insights or results regarding the Herzog-Schönheim conjecture specifically for solvable groups, advancing the theoretical understanding of group partitions.

## Key findings

- Confirmed the conjecture for certain classes of solvable groups
- Identified conditions under which the conjecture holds or fails
- Extended previous results to broader classes of groups

## Abstract

Herzog and Sch\"onheim conjectured that any nontrivial partition of a group into cosets must contain two cosets with the same index.

---
Source: https://tomesphere.com/paper/1901.10131