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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Describing free groups


Authors: J. Carson, V. Harizanov, J. Knight, K. Lange, C. McCoy, A. Morozov, S. Quinn, C. Safranski and J. Wallbaum
Journal: Trans. Amer. Math. Soc. 364 (2012), 5715-5728
MSC (2010): Primary 03C57
Published electronically: June 21, 2012
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Abstract: We consider countable free groups of different ranks. For these groups, we investigate computability theoretic complexity of index sets within the class of free groups and within the class of all groups. For a computable free group of infinite rank, we consider the difficulty of finding a basis.


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Additional Information

J. Carson
Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556

V. Harizanov
Affiliation: Department of Mathematics, George Washington University, Washington, DC 20052

J. Knight
Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556

K. Lange
Affiliation: Department of Mathematics, Wellesley College, Wellesley, Massachusetts 02482

C. McCoy
Affiliation: Department of Mathematics, University of Portland, Portland, Oregon 97203

A. Morozov
Affiliation: Sobolev Mathematical Institute, Russian Academy of Sciences, Novosibirsk 630090 Russia

S. Quinn
Affiliation: Department of Mathematics, Dominican University, River Forest, Illinois 60305

C. Safranski
Affiliation: Department of Mathematics, Saint Vincent College, Latrobe, Pennsylvania 15650

J. Wallbaum
Affiliation: Department of Mathematical Sciences, Eastern Mennonite University, Harrisonburg, Virginia 22802

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05456-0
PII: S 0002-9947(2012)05456-0
Received by editor(s): July 1, 2009
Received by editor(s) in revised form: August 25, 2010
Published electronically: June 21, 2012
Additional Notes: The authors acknowledge partial support under NSF Grant # DMS-0554841. The second author also received partial support under NSF Grant # DMS-0904101
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.