For a general description of homomorphisms, we refer to chapter MAPPINGS. This section describes some special aspects of homomorphisms whose domain or codomain is an automatic group.
Groups in the category GrpAtc currently are accepted as codomains only in some special situations. The most important cases in which an automatic group can be used as a codomain are group homomorphisms whose domain is in one of the categories GrpFP, GrpGPC, GrpRWS or GrpAtc.
Returns the homomorphism from the automatic group A to the group G defined by the expression S which can be the one of the following:[Next][Prev] [Right] [Left] [Up] [Index] [Root]It is the user's responsibility to ensure that the provided generator images actually give rise to a well-defined homomorphism. No checking is performed by the constructor.
- (i)
- A list, sequence or indexed set containing the images of the n generators A.1, ..., A.n of A. Here, the i-th element of S is interpreted as the image of A.i, i.e. the order of the elements in S is important.
- (ii)
- A list, sequence, enumerated set or indexed set, containing n tuples <xi, yi> or arrow pairs xi - > yi, where xi is a generator of A and yi∈G (i=1, ..., n) and the set {x1, ..., xn} is the full set of generators of A. In this case, yi is assigned as the image of xi, hence the order of the elements in S is not important.
Note that it is currently not possible to define a homomorphism by assigning images to the elements of an arbitrary generating set of A.