Pith Number

pith:LYFXFRYY

pith:2026:LYFXFRYYU3EE6ROLOZGJIPZUDO

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On minimal non-sofic and $\omega$-non-sofic groups

K{\i}van\c{c} Ersoy

If a minimal non-sofic group has a finitely generated residually finite maximal normal subgroup, then that subgroup is central and the group is a perfect central extension of a finitely generated non-amenable simple group.

arxiv:2604.19174 v3 · 2026-04-21 · math.GR

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Claims

C1strongest claim

if G is a minimal non-sofic group and M is a finitely generated residually finite maximal normal subgroup of G, then M is central and G is a perfect central extension of a finitely generated non-amenable simple group

C2weakest assumption

The paper assumes the existence of non-sofic groups and, for the minimal case, the existence of a finitely generated residually finite maximal normal subgroup M whose properties can be analyzed via residual finiteness and centrality (abstract, paragraph on minimal non-sofic groups)

C3one line summary

Assuming non-sofic groups exist, minimal non-sofic groups with a finitely generated residually finite maximal normal subgroup are perfect central extensions of finitely generated non-amenable simple groups, and locally graded non-sofic groups are ω-non-sofic with nontrivial profinite residual chains

References

13 extracted · 13 resolved · 0 Pith anchors

[1] M. Gromov. Endomorphisms of symbolic algebraic varieties.J. Eur. Math. Soc. (JEMS), 1(2):109–197, 1999 1999

[2] V. Capraro and M. Lupini.Introduction to Sofic and Hyperlinear Groups and Connes’ Embedding Conjecture. Lecture Notes in Mathematics 2136. Springer, Cham, 2015 2015

[3] B. H. Neumann. Some remarks on infinite groups.J. Lond. Math. Soc., 12:120–127, 1937 1937

[4] Brescia, K.ıvanç Ersoy, and M 2025

[5] S. V. Ivanov and A. Yu. Ol’shanskii. Some applications of graded diagrams in com- binatorial group theory. InGroups, Vol. 2, Proc. Int. Conf., St. Andrews/UK 1989, London Math. Soc. Lecture Note Ser. 1989

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:01:41.539370Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5e0b72c718a6c84f45cb764c943f341b924fa110a3daad8fab1227584f0e98d4

Aliases

arxiv: 2604.19174 · arxiv_version: 2604.19174v3 · doi: 10.48550/arxiv.2604.19174 · pith_short_12: LYFXFRYYU3EE · pith_short_16: LYFXFRYYU3EE6ROL · pith_short_8: LYFXFRYY

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/LYFXFRYYU3EE6ROLOZGJIPZUDO \
  | 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: 5e0b72c718a6c84f45cb764c943f341b924fa110a3daad8fab1227584f0e98d4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "acbc3989d80788b09c1d71fdc6171c6e667c116a88881d09f9d4f262fb6dfd3a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2026-04-21T07:38:54Z",
    "title_canon_sha256": "f3f293ec1122cd353e4d431b24cb5ba5413a757c88dd05675ce99ee9edff6f5b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.19174",
    "kind": "arxiv",
    "version": 3
  }
}