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June 18, 2026Journal of Algebraic CombinatoricsOpen Access

Finite groups with a large normalized sum of element orders

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Authors

LILuigi IorioMTMarco Trombetti

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Overview

Randomized trial establishes supremums of normalized sums in finite groups, indicating structural properties.

Key Points

  • This research aims to identify finite groups with large normalized sums of element orders and their structural implications.
  • Defined the normalized sum of orders for finite groups
  • Compared with known groups such as D8 and A4
  • Analyzed conditions for membership in modular subgroup lattices
  • If ψ'(G) > 19/43, G belongs to a modular subgroup lattice
  • Equality case fully established for groups exceeding boundary conditions
  • Complete description of groups satisfying ψ'(G) > 31/77, answering a prior conjecture.

Cite This Study

Iorio et al. (2026) studied this question.

synapsesocial.com/papers/6a338e3f630953a74978ef77https://doi.org/10.1007/s10801-026-01557-0
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