User:DWIII/sandbox

-- Hasse diagram for group-like structures: - * {NOTE: A quasigroup with associativity (equivalently a semigroup with divisors) automatically HAS an identity element, and is therefore a group.} - -        MAGMA    associativity->  SEMIGROUP \                                                               \           |     \                                                        |       \           |   inverse                                                    |     inverse |      \                                                      |         \           |        \                                                     |          \           |          QUASIGROUP   ---associativity---*    } |                                                             |           |     }        identity         |                                            identity        |      } |            |                                                |           |      }           |             |                                                |           |      }           |             |                                                |           |      }           |         identity                                             |           |      } |            |                                                |           |       }           V             |                                                V           |        }   * |                                                           |       }        UNITAL   |--associativity--->  MONOID         |      } \        |                                                    \       |      }                \        |                                                     \      |      }              inverse    |                                                  inverse   |      } \     V                                                       \    V      } \                                                             \         }                      LOOP    -associativity--->    GROUP  } - - --