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// Copyright (C) 1998 The New York Group Theory Cooperative
// See magnus/doc/COPYRIGHT for the full notice.
//
// Principal Author: Dmitry Pechkin
//
// Status: in progress
//
// Revision History:
//
Check-in type: amalgamated product of free groups
Objects highlighted: map M
Other objects present: group G
Name in the menu: Extend M to a homomorphism
Problem type: problem object
Help file: ExtendToHomProblem.help
Fast checks:
1. If the range group has MSC-property:
a) If images of the relators of the domain group are not trivial
in the range group
return no.
b) If the domain group is an abelian or a nilpotent group
and commutators of the generators of the domain group
are not trivial in the range group
return no.
c) Return yes.
2. If the range group is one-relator:
a) If images of the relators of the domain group are not trivial
in the range group
return no.
b) If the domain group is an abelian or a nilpotent group
and commutators of the generators of the domain group
are not trivial in the range group
return no.
c) Return yes.
3. If the domain group is free abelian and the range group is abelian group
return yes.
Algorithms:
1. For the use of this problem
2. Compute abelian invariants of G
Remarks:
// @dp This problem finds the canonical decomposition for G abelianized
// but does nothing else and remains still working.
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