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Automorphism groups of finite groupoids

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Abstract

Given a finite set M of size n and a subgroup G of Sym(M), G is pertinent iff it is the automorphism group of some groupoid 〈M; *〉. We examine when subgroups of Sym(M) are and are not pertinent. For instance, A n , the alternating group on M, is not pertinent for n > 4. We close by indicating a natural extension of our ideas, which relates to a question of M. Gould.

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Authors and Affiliations

  1. Mathematics Department, SUNY College at New Paltz, New Paltz, NY, 12561, U.S.A.

    David Hobby & Donald Silberger

  2. Mathematics Department, Hofstra University, Hempstead, NY, 11549, U.S.A.

    Sylvia Silberger

Authors
  1. David Hobby
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  2. Donald Silberger
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  3. Sylvia Silberger
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Correspondence to David Hobby.

Additional information

Presented by K. Kearnes.

Our work benefited from our conversations with David Clark, Jacqueline R. Grace, William V. Grounds, and Allan J. Silberger.

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Hobby, D., Silberger, D. & Silberger, S. Automorphism groups of finite groupoids. Algebra Univers. 64, 117–136 (2010). https://doi.org/10.1007/s00012-010-0093-0

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  • DOI: https://doi.org/10.1007/s00012-010-0093-0

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