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Arboreal Group Theory pp 355–368Cite as

Foldings of G-trees

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Part of the book series: Mathematical Sciences Research Institute Publications ((MSRI,volume 19))

Abstract

The theory of group actions on trees is used to produce a proof of Grushko’s theorem, which extends to a theorem involving amalgamated free products; this mimics the author’s topological proof, but some new consequences are drawn. Theorems of Shenitzer and Swarup on amalgamations and HNN-extensions over cyclic subgroups are deduced as a consequence and somewhat generalized.

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References

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Author information

Authors and Affiliations

  1. Mathematics Department, University of California, Berkeley, CA, 94720, USA

    John R. Stallings

Authors
  1. John R. Stallings
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Editor information

Editors and Affiliations

  1. Department of Mathematics and Computer Science, San Jose State University, San Jose, 95192, California, USA

    Roger C. Alperin

  2. Mathematical Sciences Research Institute, 1000 Centennial Drive, Berkeley, CA, 94720, USA

    Roger C. Alperin

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© 1991 Springer-Verlag New York, Inc.

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Stallings, J.R. (1991). Foldings of G-trees. In: Alperin, R.C. (eds) Arboreal Group Theory. Mathematical Sciences Research Institute Publications, vol 19. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3142-4_14

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  • DOI: https://doi.org/10.1007/978-1-4612-3142-4_14

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7811-5

  • Online ISBN: 978-1-4612-3142-4

  • eBook Packages: Springer Book Archive

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