Pith Number

pith:GVOUSS4C

pith:2025:GVOUSS4CMWXSKHPGXS3YOISHIM

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The profinite genus of the groups $\mathbb{Z}^n\rtimes C_{p^2}$

Anderson Porto, John MacQuarrie, Marlon Estanislau

A formula gives the profinite genus of every group of the form Z^n semidirect product C_{p squared}.

arxiv:2511.22658 v2 · 2025-11-27 · math.GR

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Record completeness

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4 Citations open

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Claims

C1strongest claim

A formula is given for the profinite genus of groups of the form Z^n ⋊ C_{p²}, completing the calculation of the size of the genus of semidirect products of the form Z^n ⋊ G where G is a finite p-group of finite integral representation type.

C2weakest assumption

The calculation assumes that the groups are exactly of the stated semidirect product form and that the prior results on finite integral representation type for the p-groups remain valid without additional restrictions.

C3one line summary

A formula is given for the profinite genus of Z^n ⋊ C_{p²}, completing the genus size calculation for Z^n ⋊ G where G is any finite p-group of finite integral representation type.

References

18 extracted · 18 resolved · 0 Pith anchors

[1] G. Baumslag. Residually finite groups with the same finite images.Compositio Mathematica, 29(3):249–252, 1974 1974

[2] C. W. Curtis and I. Reiner.Methods of Representation Theory - with applications to finite groups and orders, volume I. John Wiley & Sons, New York, 1990 1990

[3] V . R. de Bessa, F. Grunewald, and P . A. Zalesskii. Genus for virtually surface groups and pullbacks.Manuscripta Mathematica, 145:221–233, 2014 2014

[4] V . R. de Bessa, A. L. P . Porto, and P . A. Zalesskii. The profinite completion of accessible groups.Monatsh. Math., 202(2):217–227, 2022 2022

[5] V . R. de Bessa, A. L. P . Porto, and P . A. Zalesskii. Profinite genus of free products with finite amalgamation.Journal of Algebra, 643:11–48, 2024 2024

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T03:10:11.724106Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

355d494b8265af251de6bcb78722474326d9bc48e2a818b4078756b06040ccf1

Aliases

arxiv: 2511.22658 · arxiv_version: 2511.22658v2 · doi: 10.48550/arxiv.2511.22658 · pith_short_12: GVOUSS4CMWXS · pith_short_16: GVOUSS4CMWXSKHPG · pith_short_8: GVOUSS4C

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/GVOUSS4CMWXSKHPGXS3YOISHIM \
  | 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: 355d494b8265af251de6bcb78722474326d9bc48e2a818b4078756b06040ccf1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8f017c2e3ac1e9ea74487017ee79fc04b5b7d0ba5f2be5058750a1c72787e0bb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2025-11-27T17:49:49Z",
    "title_canon_sha256": "feb45541670b27e6a6df0aaa9c8e85a418d99f91219a4914fed932c50c517460"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2511.22658",
    "kind": "arxiv",
    "version": 2
  }
}