| 31. | The identity element is represented by the empty set.
|
| 32. | Such identity elements have been used both in establishing theory and in computations; see below.
|
| 33. | Many also have identity elements and inverse elements.
|
| 34. | A semigroup has an " associative " binary operation, but might not have an identity element.
|
| 35. | A trivial torsor corresponds to the identity element.
|
| 36. | There can be ambiguity when two cycles share an element that is not the identity element.
|
| 37. | The additive identity element is of course zero.
|
| 38. | Reflection groups are necessarily achiral ( except for the trivial group containing only the identity element ).
|
| 39. | This defines a group in which the identity element is and the inverse of the element is.
|
| 40. | The identity element for multiplication is 1.
|
