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The Schur multiplicator of metacyclic groups


Author: F. Rudolf Beyl
Journal: Proc. Amer. Math. Soc. 40 (1973), 413-418
MSC: Primary 20D10
DOI: https://doi.org/10.1090/S0002-9939-1973-0325759-7
Addendum: Proc. Amer. Math. Soc. 43 (1974), 251-252.
MathSciNet review: 0325759
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Abstract: The Schur multiplicator $ {H_2}G$ of a (finite) metacyclic group $ G$ is computed with the help of the Lyndon spectral sequence. The order of $ {H_2}G$ is a useful invariant of $ G$. A metacyclic group with vanishing Schur multiplicator can be presented with two generators and two relators. A simple description of the totality of these groups is given and all such $ p$-groups are classified.


References [Enhancements On Off] (What's this?)

  • [1] F. R. Beyl, The classification of metacyclic $ p$-groups (to appear).
  • [2] D. B. A. Epstein, Finite presentations of groups and $ 3$-manifolds, Quart. J. Math. Oxford Ser. (2) 12 (1961), 205-212. MR 26 #1867. MR 0144321 (26:1867)
  • [3] P. J. Hilton and U. Stammbach, A course in homological algebra, Graduate Texts in Math. 4, Springer-Verlag, New York and Berlin, 1971. MR 0346025 (49:10751)
  • [4] I. Schur, Untersuchungen über die Darstellungen der endlichen Gruppen durch gebrochene lineare Substitutionen, J. Reine Angew. Math. 132 (1907), 85-137.
  • [5] J. W. Wamsley, The deficiency of metacyclic groups, Proc. Amer. Math. Soc. 24 (1970), 724-726. MR 41 #3576. MR 0258931 (41:3576)
  • [6] H. Zassenhaus, Lehrbuch der Gruppentheorie, Teubner, Leipzig, 1937; English transl., Chelsea, New York, 1949. MR 11, 77.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0325759-7
Keywords: Metacyclic group, Schur multiplicator, Schur group, deficiency, Lyndon spectral sequence
Article copyright: © Copyright 1973 American Mathematical Society

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