bibkey: tarnauceanu2024reciprocal
authors: M. Tărnăuceanu
year: 2024
title: On the sum of inverses of subgroup orders in finite groups
doi: null
url: https://www.math.uaic.ro/~martar/pdf/articole/articol%20141.pdf
claim: Conjecture 3.1 asks whether no constant c > 1 is a lower bound for the subgroup-order reciprocal sum on all finite non-cyclic groups.
strata_touched:
  - D5/S3/FiniteGroups/TarnauceanuReciprocalSubgroupOrders
license: citation-only
triage: anchor

On the sum of inverses of subgroup orders in finite groups

M. Tărnăuceanu, “On the sum of inverses of subgroup orders in finite groups,” Scientific Studies and Research, Series Mathematics and Informatics 34 (2024), no. 1, 115–120.

The paper defines f(G) as the sum of 1/|H| over the subgroup lattice and states Conjecture 3.1: “There is no constant c > 1 such that f(G) > c, for all finite non-cyclic groups G.” The paper obtains the limiting construction under the assumption that infinitely many Sophie Germain primes exist. The formal settlement uses the same split cyclic family with a growing exponent and removes that assumption by choosing a prime congruent to one modulo the acting prime.

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URL: https://www.math.uaic.ro/~martar/pdf/articole/articol%20141.pdf