Pith Number

pith:BXNPZQOA

pith:2026:BXNPZQOAVRG6HRBSYJZGLGYYHF

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On subgroups of Brin-Thompson groups $nV$

Sadayoshi Kojima, Xiaobing Sheng

The Brin-Thompson group nV is torsion locally finite for all n at least 1, and for n at least 2 it contains infinite-order elements that admit roots of arbitrarily large order.

arxiv:2603.18410 v3 · 2026-03-19 · math.GR

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\pithnumber{BXNPZQOAVRG6HRBSYJZGLGYYHF}

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Record completeness

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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

We prove that the Brin-Thompson group nV is torsion locally finite for n ≥ 1 which is known only when n = 1, and nV contains elements of infinite order admitting roots with arbitrary large order for n ≥ 2 which is known to not be true for the n = 1 case.

C2weakest assumption

The proofs rely on the standard combinatorial definition and known properties of Brin-Thompson groups nV for n=1, together with the generalization to higher n; without the full manuscript the precise steps and any hidden assumptions in the extension cannot be checked.

C3one line summary

nV is torsion locally finite for all n≥1 and for n≥2 contains infinite-order elements admitting roots of arbitrarily large order.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-26T01:03:28.307933Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0ddafcc1c0ac4de3c432c272659b18394947772383bd394dffbcfe571357d228

Aliases

arxiv: 2603.18410 · arxiv_version: 2603.18410v3 · doi: 10.48550/arxiv.2603.18410 · pith_short_12: BXNPZQOAVRG6 · pith_short_16: BXNPZQOAVRG6HRBS · pith_short_8: BXNPZQOA

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/BXNPZQOAVRG6HRBSYJZGLGYYHF \
  | 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: 0ddafcc1c0ac4de3c432c272659b18394947772383bd394dffbcfe571357d228

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b3cdc2ea1a4fe9f2c10d2151daa2be32f81c4166b241a1a64c9d05dede14231b",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2026-03-19T02:18:09Z",
    "title_canon_sha256": "c2755d1fe55e8ee0f009fc7c2b8e1a436630d33a635aed86940b1b618a8adbba"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.18410",
    "kind": "arxiv",
    "version": 3
  }
}