# Construction of an SLP-Group and its Elements

## Structure Constructors

Magma’s black-box groups are built on Magma’s other group types. The basic constructor takes a group and returns a corresponding black-box group. The element set of the black-box group is essentially the same as the element set of the original group, and the group operations are inherited from the original group.

### `NaturalBlackBoxGroup(H): Grp -> GrpBB`

Construct the natural black-box group from the concrete group $H$.

## Construction of an Element

### `Identity(G): GrpBB -> GrpBBElt`

### `Id(G): GrpBB -> GrpBBElt`

### `G ! 1: GrpBB, RngIntElt -> GrpBBElt`

Construct the identity element for the BB-group $G$.