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 
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}]