2 ms·

"Commutative" communicates something. "Abelian" communicates nothing. "Order-independent" like I suggested communicates a lot.

Someone 6y ago
Does it? I think that could describe “associative” equally well as “commutative”. Edit: “symmetric” might be an alternative for Abelian because the Cayley table (https://en.wikipedia.org/wiki/Cayley_table https://en.wikipedia.org/wiki/Cayley_table) of an Abelian group is symmetric. I’m not sure that’s immediately clear enough for laymen, though.
- ganzuul 6y ago
  Symmetric is also good but it has a very distinct geometric interpretation. If we can avoid overloading terminology in a confusing way when designing these the names we should do so. Perhaps pair-independent is a distinctive name for associative...
  - Someone 6y ago
    Well, introducing the new term “Abelian” certainly avoids overloading terminology in a confusing way :-) “Pair invariant” IMO, isn’t good, certainly worse than “Pairing invariant”. “Parentheses invariant” might work, but of course would get just as confusing/incorrect as “pair invariant” once one moves from groups to fields.
    - ganzuul 6y ago
      "Associative" doesn't provide any information to avoid confusion when dealing with mixed operators either. Somehow including "peer" in the terminology could help.
- deleted 6y ago
  [deleted]
- gizmo686 6y ago
  "Symmetric group" is already taken. Given a set S, the symmetric group G_s is the group of all permutations of S. Not to be confused with a permutation group of S, which is a group of some permutations of S. I suppose we could rename "symmetric group" to "maximal permutation group", but stringing adjectives together is not a sustainable strategy for naming. Plus, it is not clear to me how accurate "maximal permutation group" is as a name. That is, the symmetric group S_3 is the maximal permutation group of {1,2,3}. However, it is not generally a maximal permutation group, as it is contained withing the permutation group S_4.

Someone 6y ago

Does it? I think that could describe “associative” equally well as “commutative”. Edit: “symmetric” might be an alternative for Abelian because the Cayley table (https://en.wikipedia.org/wiki/Cayley_table https://en.wikipedia.org/wiki/Cayley_table) of an Abelian group is symmetric. I’m not sure that’s immediately clear enough for laymen, though.

ganzuul 6y ago
Symmetric is also good but it has a very distinct geometric interpretation. If we can avoid overloading terminology in a confusing way when designing these the names we should do so. Perhaps pair-independent is a distinctive name for associative...
- Someone 6y ago
  Well, introducing the new term “Abelian” certainly avoids overloading terminology in a confusing way :-) “Pair invariant” IMO, isn’t good, certainly worse than “Pairing invariant”. “Parentheses invariant” might work, but of course would get just as confusing/incorrect as “pair invariant” once one moves from groups to fields.
  - ganzuul 6y ago
    "Associative" doesn't provide any information to avoid confusion when dealing with mixed operators either. Somehow including "peer" in the terminology could help.
deleted 6y ago
[deleted]
gizmo686 6y ago
"Symmetric group" is already taken. Given a set S, the symmetric group G_s is the group of all permutations of S. Not to be confused with a permutation group of S, which is a group of some permutations of S. I suppose we could rename "symmetric group" to "maximal permutation group", but stringing adjectives together is not a sustainable strategy for naming. Plus, it is not clear to me how accurate "maximal permutation group" is as a name. That is, the symmetric group S_3 is the maximal permutation group of {1,2,3}. However, it is not generally a maximal permutation group, as it is contained withing the permutation group S_4.