Abstract
The well known Andrews-Curtis Conjecture [2] is still open. In this paper, we establish its finite version by describing precisely the connected components of the Andrews-Curtis graphs of finite groups. This finite version has independent importance for computational group theory. It also resolves a question asked in [5] and shows that a computation in finite groups cannot lead to a counterexample to the classical conjecture, as suggested in [5].
Original language | English |
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Title of host publication | Progress in Mathematics |
Publisher | Springer Basel |
Pages | 15-30 |
Number of pages | 16 |
DOIs | |
State | Published - 2005 |
Publication series
Name | Progress in Mathematics |
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Volume | 248 |
ISSN (Print) | 0743-1643 |
ISSN (Electronic) | 2296-505X |
Bibliographical note
Publisher Copyright:© 2005, Birkhäuser Verlag Basel/Switzerland.
Keywords
- Andrews-Curtis conjecture
- Finite group
- Generators