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A Cohomological Criterion for a Finitely Presented Group to be Infinite
Author(s) -
Holt D. F.,
Plesken W.
Publication year - 1992
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-45.3.469
Subject(s) - citation , mathematics , group (periodic table) , algebra over a field , library science , combinatorics , computer science , pure mathematics , physics , quantum mechanics
The problem of proving that a given finitely presented group G is infinite can be very difficult (or impossible) in general, but there are several possible approaches that can be tried, some of which can be rendered much more effective with the assistance of computers. To this list, we add another one, which can be applied if an epimorphism of G onto a finite group H is known. The idea depends on the following criterion.