Pith Number

pith:5SBIEKMC

pith:2026:5SBIEKMCJ6RVXZIFE4ITQ2GZ2R

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Maximally almost periodic subgroups of Abelian groups of prime exponent

Ol'ga Sipacheva

Any infinite Abelian topological group of prime exponent contains an infinite maximally almost periodic subgroup.

arxiv:2605.17495 v1 · 2026-05-17 · math.GN · math.GR

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Claims

C1strongest claim

It is proved that any infinite Abelian topological group of prime exponent has an infinite maximally almost periodic subgroup.

C2weakest assumption

The group is assumed to be infinite, Abelian, topological, and of prime exponent; if any of these structural hypotheses fails, the existence statement does not apply (abstract).

C3one line summary

Any infinite Abelian topological group of prime exponent has an infinite maximally almost periodic subgroup.

References

8 extracted · 8 resolved · 0 Pith anchors

[1] Cardinal invariants of topological groups. Embeddings and con- densations, 1979

[2] A. Arhangel’skii and M. Tkachenko,Topological Groups and Related Structures, (At- lantis Press, Amsterdam, 2008) 2008

[3] The theory of topological groups I, 1950

[4] Engelking,General Topology, 2nd ed 1989

[5] Fuchs,Infinite Abelian Groups(Academic Press, New York, 1970), Vol 1970

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:04:42.149214Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ec828229824fa35be50527113868d9d478aa6ec8d002e8d95b6ba958045e61cc

Aliases

arxiv: 2605.17495 · arxiv_version: 2605.17495v1 · doi: 10.48550/arxiv.2605.17495 · pith_short_12: 5SBIEKMCJ6RV · pith_short_16: 5SBIEKMCJ6RVXZIF · pith_short_8: 5SBIEKMC

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/5SBIEKMCJ6RVXZIFE4ITQ2GZ2R \
  | 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: ec828229824fa35be50527113868d9d478aa6ec8d002e8d95b6ba958045e61cc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b561fa295322aca07cf0870c1229aeb6941660e37e5318467b1433c923637088",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GN",
    "submitted_at": "2026-05-17T15:12:13Z",
    "title_canon_sha256": "ab63733ae6c7a75cb6eb43e28c335b20953aa5b3e8ca4f45a8845566108463c8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17495",
    "kind": "arxiv",
    "version": 1
  }
}