// 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 finite ?

Problem type:		problem object

Help file:		IsFiniteProblem.help


			     Fast checks:


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

2. If there exists a generator with zero exponent sum in every relator
   of the group
  	return no


			     Algorithms:


1. Compute the torsion-free rank of the abelianization of G
  
2. Seek a rewriting system for G

3. 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.

  



