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Tools: Presentations and Their Calculus

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Lectures on Finitely Generated Solvable Groups

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Abstract

We introduce group presentations, present Von Dyck’s lemma and Tietze’s theorem on their transformations. We bring in an important result by B.H. Neumann about finitely presentable groups.

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References

  1. Atiyah, M.F., Macdonald, I.G.: Introduction to Commutative Algebra. Addison-Wesley, Reading (1969)

    MATH  Google Scholar 

  2. Baumslag, G.: On finitely presented metabelian groups. Bull. Amer. Math. Soc.78(2), 279 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  3. Baumslag, G.: Subgroups of finitely presented metabelian groups. J. Austral. Math. Soc.16, 98–110 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  4. Baumslag, G., Cannonito, F.B., Miller, C.F., III: Infinitely generated subgroups of finitely presented groups. II. Math. Z.172(2), 97–105 (1980)

    MathSciNet  MATH  Google Scholar 

  5. Baumslag, G., Cannonito, F.B., Robinson, D.J.S.: The algorithmic theory of finitely generated metabelian groups. Tran. Amer. Math. Soc.344(2), 629–648 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  6. Baumslag, G., Mikhailov, R., Orr, K.E.: A new look at finitely generated metabelian groups, arXiv:1203.5431v1 [math.GR] 24 Mar 2012

    Google Scholar 

  7. Bieri, R., Strebel, R.: Almost finitely presented soluble groups. Comment. Math. Helv.53, 258–278 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  8. Hall, P.: Finiteness conditions for soluble groups. Proc. London Math. Soc.4, 419–436 (1954)

    Article  MathSciNet  MATH  Google Scholar 

  9. Hall, P.: On the finiteness of certain soluble groups. Proc. London Math. Soc.3, 595–622 (1959)

    Article  Google Scholar 

  10. Hall, P.: The Frattini subgroups of finitely generated groups. Proc. London Math. Soc.3, 327–352 (1961)

    Article  Google Scholar 

  11. Higman, G.: Subgroups of finitely presented groups. Proc. Roy. Soc. Ser. A262, 455–475 (1961)

    Article  MathSciNet  MATH  Google Scholar 

  12. Krasner, M., Kaloujnine, L.: Produit complet des groupes de permutations et probleme dextension des groupes. Acta Sci. Mz. Szeged13, 208–230 (1950);14, 39–66 and 69–82 (1951)

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Manhattan College, New York, NY, USA

    Katalin A. Bencsáth

  2. Department of Applied Mathematics and Computer Science New York City College of Technology, The City University of New York, Brooklyn, NY, USA

    Marianna C. Bonanome

  3. Department of Mathematics Borough of Manhattan Community College, The City University of New York, New York, NY, USA

    Margaret H. Dean & Marcos Zyman

Authors
  1. Katalin A. Bencsáth
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  2. Marianna C. Bonanome
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  3. Margaret H. Dean
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  4. Marcos Zyman
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© 2013 Katalin A. Bencsath, Marianna C. Bonanome, Margaret H. Dean, Marcos Zyman

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Bencsáth, K.A., Bonanome, M.C., Dean, M.H., Zyman, M. (2013). Tools: Presentations and Their Calculus. In: Lectures on Finitely Generated Solvable Groups. SpringerBriefs in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-5450-2_2

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