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algebra / Group theory

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 $23984$.

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algebraJul 20, 2026Significance 15/100Registry: lean verified

Kourovka Problem 19.25 - Totient Sums and Simplicity

Prior state unknown→disproved

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 $23984$.

Source authenticatedKourovka Problem 19.25 - Totient Sums and Simplicity →
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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 $23984$.

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