The assumption in Britton's lemma is that the word is equal to this. Any element of a coset H acts as one
 of these for H. In a group, if an element is of this type, it must commute with all other group elements and
 furthermore there is only one of these elements in a group
The assumption in Britton's lemma is that the word is equal to this. Any element of a coset H acts as one
 of these for H. In a group, if an element is of this type, it must commute with all other group elements and
 furthermore there is only one of these elements in a group. This is the result of a function composed with its
 inverse. In algebra, there are usually written as e. For matrices, this a matrix with ones down the diagonal
 and zeros elsewhere. For 10 points, name these elements and functions that preserve the operand
 exemplified by how one times any integer b is b.
The assumption in Britton's lemma is that the word is equal to this.
{identity} element [or {identity} function; or {identity map}]