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Remarks on free Bieberbach groups

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Abstract

Recent results on the Gupta representation of the unique stem cover of a free Bieberbach group lead to explicite determination of its Schur multiplicator. The aim of this note is to estimate the free-abelian rank of the Schur multiplicator, using only the 8-term Eckmann-Hilton-Stammbach exact homology sequence induced by the free Bieberbach group modulo its nontrivial center. The note ends with a discussion about the structure of torsion-free Bieberbach groups constructed by S.Rosset.

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References

  1. Beyl,F.R., Felgner,U. and Schmid,P.: On groups occuring as center factor groups. J. Algebra61, 161–177(1979)

    Article  Google Scholar 

  2. Bieri,R.: Normal subgroups in duality groups and in groups of cohomological dimension 2. J.Pure Appl.Algebra7, 35–51(1976)

    Article  Google Scholar 

  3. Eckmann,B., Hilton,P.J. and Stammbach,U.: On the homology theory of central group extensions II. The exact sequence in the general case. Comm.Math.Helv.47,171–178 (1972)

    Google Scholar 

  4. Farkas,D.R.: Miscellany on Bieberbach algebras. Pacific J.Math.59,427–435(1975)

    Google Scholar 

  5. Gupta,N.: Certain commutator subgroups of free groups. Comm.Pure Appl.Math.26,699–702 (1973)

    Google Scholar 

  6. Ojanguren,M.: Freie Präsentierungen endlicher Gruppen und zugehörige Darstellungen. Math.Z.106,293–311(1968)

    Article  Google Scholar 

  7. Rosset,S.: Group extensions and division algebras. J.Algebra53,297–303(1978)

    Article  Google Scholar 

  8. Stöhr,R.: On Gupta representations of central extensions. Math.Z.187,259–267(1984)

    Article  Google Scholar 

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  1. Department of Mathematical Sciences, National Chengchi University, Mucha, Taipei, 11623, Taiwan, Republic of China

    Eng Tjioe Tan

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  1. Eng Tjioe Tan
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Tan, E.T. Remarks on free Bieberbach groups. Manuscripta Math 60, 477–486 (1988). https://doi.org/10.1007/BF01258665

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  • DOI: https://doi.org/10.1007/BF01258665

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