Kourovka Problem 19.25 - Totient Sums and Simplicity

Do a finite group's order together with $\sum_{g \in G} \varphi(|g|)$ determine whether the group is simple? A simple and a non-simple group of order $6048$ share the statistic $23984$.

Result

Disproved

Status

Resolved

AI contribution

AI-discovered

Method

Argument

Field

Group theory

Posed by

—

Year posed

2018

Years open

8y

Solved

2026-07-20

Model

Aristotle

Vendor

Harmonic

Collaborators

—

Verification

Lean-verified

Publication

Preprint

Significance

15 / 100*

Disclosed cost

—

Wikipedia

No dedicated article