Specification: Permutation Group Elements (OSCAR v1.2-v1.3)

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

In OSCAR v1.2 and v1.3, PermGroupElem still uses the bare type name, and its parent group follows the PermGroup variant with nested data.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", "1.3.1"]},
  "_type": {"name": "PermGroupElem", "params": "6a860ea3-b10e-47d2-9634-5166c9257b23"},
  "data": ["2", "1"],
  "_refs": {
    "6a860ea3-b10e-47d2-9634-5166c9257b23": {
      "_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