Pith Number

pith:Y7I7TWEU

pith:2026:Y7I7TWEU623X2KEEESSFRFMIO6

not attested not anchored not stored refs resolved

Finite groups with a large normalized sum of element orders

Luigi Iorio, Marco Trombetti

If the normalized sum of element orders in a finite group exceeds 19/43, the value for the dihedral group of order 8, then the group has a modular subgroup lattice.

arxiv:2601.11253 v2 · 2026-01-16 · math.GR

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\usepackage{pith}
\pithnumber{Y7I7TWEU623X2KEEESSFRFMIO6}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

if ψ'(G)>ψ'(D_8) = 19/43, then G belongs to the well-understood class of groups with a modular subgroup lattice, whose structure theory allows us to readily identify all groups satisfying this bound

C2weakest assumption

The critical threshold is exactly ψ'(D8), which is assumed to be the largest value attained by groups outside the modular-lattice class; this relies on exhaustive case analysis or classification results for small-order groups that are not detailed in the abstract.

C3one line summary

Finite groups with ψ'(G) > 19/43 have modular subgroup lattices; all groups with ψ'(G) > 31/77 are classified, completing the supersolubility criterion.

References

13 extracted · 13 resolved · 0 Pith anchors

[1] Sums of element orders in finite groups 2009

[2] A criterion for solvability of a finite group by the sum of element orders 2018

[3] On two conjectures about the sum of element orders 2022

[4] A result on the sum of element orders of a finite group 2020

[5] GAP – Groups, Algorithms, and Programming 2024

Receipt and verification

First computed	2026-05-18T02:44:31.941994Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c7d1f9d894f6b77d288424a4589588778cd4f4b4800eb4d0493b3d580ac84622

Aliases

arxiv: 2601.11253 · arxiv_version: 2601.11253v2 · doi: 10.48550/arxiv.2601.11253 · pith_short_12: Y7I7TWEU623X · pith_short_16: Y7I7TWEU623X2KEE · pith_short_8: Y7I7TWEU

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/Y7I7TWEU623X2KEEESSFRFMIO6 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: c7d1f9d894f6b77d288424a4589588778cd4f4b4800eb4d0493b3d580ac84622

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0f4b861e9de2b0c2cd4e4ba8b20dc6523109479377a3612581c7ffc22b9dd023",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2026-01-16T13:01:49Z",
    "title_canon_sha256": "78d900b982eb33598205cf3749a7765ab6a86fb91852deddc312b01a6a995fd2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2601.11253",
    "kind": "arxiv",
    "version": 2
  }
}