Specification: Pc Group Elements (OSCAR v1.1-v1.3)

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

In OSCAR v1.1 through v1.3, PcGroupElem keeps the bare type name "PcGroupElem", but its parent group is referenced through _refs.

Encoding Notes

• Use _type: "PcGroupElem".
• Store the exponent vector under data.
• Refer to the parent group through a reference id in the parameters.

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": "PcGroupElem", "params": "19829e6e-a8a7-42d6-a7c6-ed1fb1a95718"},
  "data": ["1", "0", "0", "0"],
  "_refs": {
    "19829e6e-a8a7-42d6-a7c6-ed1fb1a95718": {"_type": "PcGroup", "data": {"X": "2d5459cc-e6d8-4e32-aff1-bd1c52b81a5b"}},
    "2d5459cc-e6d8-4e32-aff1-bd1c52b81a5b": {
      "_type": "GapObj",
      "data": {
        "GapType": "IsPcGroup",
        "relord": ["2", "3", "2", "2"],
        "power_rels": [],
        "comm_rels": [
          ["2", "1", ["2", "1"]],
          ["3", "1", ["3", "1", "4", "1"]],
          ["4", "1", ["3", "1", "4", "1"]],
          ["3", "2", ["3", "1", "4", "1"]],
          ["4", "2", ["3", "1"]]
        ]
      }
    }
  }
}

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 pc group