Specification: Permutation Group Elements (OSCAR v1.4-v1.5)

Profiles: OSCAR v1.4, OSCAR v1.5 Other versions: Permutation Group Elements (OSCAR v1.0-v1.1), Permutation Group Elements (OSCAR v1.2-v1.3), Permutation Group Elements (OSCAR v1.6-v1.8)

In OSCAR v1.4 and v1.5, PermGroupElem still uses the bare type name, and its parent group follows the PermGroup variant with top-level attrs.

Encoding Notes

• Use _type: "PermGroupElem".
• Store the permutation word under data.
• Refer to the parent group according to the matching PermGroup encoding.

Canonical Example Payload

The following payload is taken directly from the current rosetta-stone corpus.

{
  "_ns": {"Oscar": ["https://github.com/oscar-system/Oscar.jl", "1.5.1"]},
  "_type": {"name": "PermGroupElem", "params": "1da577a2-a6ab-48de-a976-7fb3d69551fd"},
  "data": ["2", "1"],
  "_refs": {
    "1da577a2-a6ab-48de-a976-7fb3d69551fd": {
      "_type": "PermGroup",
      "data": {"degree": "5", "gens": [["2", "1"], ["1", "2", "4", "3"], ["3", "4", "1", "2"]]},
      "attrs": {
        "order": {"_type": "ZZRingElem", "data": "8"},
        "is_nilpotent": {"_type": "Bool", "data": "true"},
        "is_perfect": {"_type": "Bool", "data": "false"},
        "is_solvable": {"_type": "Bool", "data": "true"}
      }
    }
  }
}

Documented Profiles in This Corpus

This table records the profile/version pairs currently represented by the rosetta-stone examples for this data type. Add new rows as new systems or encoding revisions are documented.

Rosetta Stone Examples

• Element of subgroup of symmetric group
• Element of symmetric group