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Grün’s theorems and class groups

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In this article we show how Grün’s results in group theory can be used for studying the structure of class groups in normal extensions.

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References

  1. Benjamin E., Lemmermeyer F., Snyder C.: Imaginary quadratic fields with Cl2(k) = (2, 2, 2), J. Number Theory 103, 38–70 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  2. Grün O.: Über Substitutionsgruppen im Galoisfeld G(p f). J. Reine Angew. Math. 171, 170–172 (1934)

    Google Scholar 

  3. Grün O.: Beiträge zur Gruppentheorie. I.. J. Reine Angew. Math. 174, 1–14 (1935)

    MATH  Google Scholar 

  4. Lemmermeyer F.: On the 2-class field towers of some imaginary quadratic number fields. Abh. Math. Sem. Hamburg 67, 205–214 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  5. Lemmermeyer F.: Galois action on class groups. J. Algebra 264, 553–564 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  6. Metsänkylä T.: On the history of the study of ideal class groups. Expo. Math. 25, 325–340 (2007)

    MathSciNet  MATH  Google Scholar 

  7. Nover H.: Computation of Galois groups associated to the 2-class towers of some imaginary quadratic fields with 2-class group C 2 × C 2 × C 2. J. Number Theory 129, 231–245 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  8. Roquette P.: From FLT to finite groups. The remarkable career of Otto Grün. Jahresber. Dtsch. Math.-Ver. 107, 117–154 (2005)

    MathSciNet  MATH  Google Scholar 

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Correspondence to Franz Lemmermeyer.

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Lemmermeyer, F. Grün’s theorems and class groups. Arch. Math. 96, 135–138 (2011). https://doi.org/10.1007/s00013-010-0193-2

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