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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Describing free groups
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by J. Carson, V. Harizanov, J. Knight, K. Lange, C. McCoy, A. Morozov, S. Quinn, C. Safranski and J. Wallbaum PDF
Trans. Amer. Math. Soc. 364 (2012), 5715-5728 Request permission


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
  • MR Author ID: 103325
  • K. Lange
  • Affiliation: Department of Mathematics, Wellesley College, Wellesley, Massachusetts 02482
  • C. McCoy
  • Affiliation: Department of Mathematics, University of Portland, Portland, Oregon 97203
  • MR Author ID: 695683
  • 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
  • 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
  • © Copyright 2012 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 364 (2012), 5715-5728
  • MSC (2010): Primary 03C57
  • DOI:
  • MathSciNet review: 2946928