If a relation can be derived from the remaining generators, remove fronm the list of relations.
If is a word in the generators and , then add to the list of generators and to the list of relations.
If a relation takes the form , where is a generator and is a word in generators other than , then remove from the list of relations, replace all occurences of in the remaining relations by and remove from the list of generators.
Note that transforms 1 and 2 are inverse to each other and likewise 3 and 4 are inverses. More generally, the term “Tietze transform” referes to a transform which can be expressed as the compositon of a finite number of the four transforms listed above. By way of contrast, the term “elementary Tietze transformation” is used to denote the four transformations given above and the term “general Tietze transform” could be used to indicate a member of the larger class.
Tieze showed that any two presentations of the same finitely presented group differ by a general Tietze transform.
|Date of creation||2013-03-22 15:42:40|
|Last modified on||2013-03-22 15:42:40|
|Last modified by||rspuzio (6075)|
|Defines||elementary Tietze transformation|
|Defines||general Tietze transform|