// Copyright (C) 1998 The New York Group Theory Cooperative
// See magnus/doc/COPYRIGHT for the full notice.
//
// Principal Author: Dmitry Bormotov
//
// Status: in progress
//
// Revision History:
//


Check-in type:		finitely presented group

Objects highlighted:	group G 

Name in the menu:	Is G trivial ?

Problem type:		problem object

Help file:		IsTrivialProblem.help


			     Fast checks:


1. If G = < ; > 
	return yes

2. If the number of relators is less than the number of generators
     	return no

3. If there exists a generator with zero exponent sum in every relator
   of the group
  	return no
 
4. If the greatest common divisor of exponent sums of some generator
   in the group relations is bigger than one
	return no


			     Algorithms:


1. For the use of this problem
  
2. Is abelianization of G trivial ?
  
3. Enumerate normal closure of relators
  
4. Seek a rewriting system for G

5. Seek a ShortLex automatic structure for G
	
   Links:
	
	Click here to see a word acceptor.

	Click here to the first difference machine.

	Click here to the second difference machine.

	Click here to the general multiplier.

6. Run genetic algorithm

7. Compute lower central quotients for G
  
8. Solve using lower central quotients of G
  
  



