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Group Theoretical Methods in Physics pp 348–356Cite as

A chemist looks at the structure of symmetry groups

On a generic scheme of important point groups for rigid molecular frames

  • Atomic, Molecular, Nuclear, Solid State Physics
  • Conference paper
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Part of the book series: Lecture Notes in Physics ((LNP,volume 50))

Abstract

A practical method for generating larger symmetry groups from smaller ones is presented. It is based upon the construction of the abstract-unique group H(G) called the holomorph of a given starting group G. The extension of G by its full automorphism group A(G) is given in great detail as permutation realizations for both the cyclic and the abelian group of order 4. A selection of point groups generated by this method of the holomorph is given for some important symmetries.

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References.

  1. D.J.Klein, C.H.Carlisle, and F.A.Matsen, Adv.Quant.Chem. (P.-O. Löwdin, ed.) 5,219 (1970).

    Google Scholar 

  2. G.A.Gallup, ibid. 7,113 (1973)

    Google Scholar 

  3. J.Serre, ibid. 8,1 (1974).

    Article  Google Scholar 

  4. H.C.Longuet-Higgins, Molec.Phys. 6,445 (1963).

    Google Scholar 

  5. H.P.Fritzer, Lectures on “The Symmetric Group Sm in Modern Chemistry”, Univ.East Anglia (England), Aug./Sept. 1974.

    Google Scholar 

  6. W.Burnside, Theory of Groups of finite order, Dover, 1955.

    Google Scholar 

  7. See any standard text on group theory.

    Google Scholar 

  8. O.Schreier, Mh.Math.Phys. 12,165 (1926); M.Hall, Ann.Math.39, 220 (1938).

    Google Scholar 

  9. F.Herbut,M.Vujičić,I.Božović,and Dj.Ŝijački, Proc.3rd Intern. Coll.Group theoretical methods in physics, Marseille 1974, (A.Janner and T.Jannssen, eds.), Nijmegen University Press, p.441,447 and 577 in Vol.2, and refs. therein.

    Google Scholar 

  10. S.L.Altmann, Phil.Trans.Roy.Soc., a255, 216 (1963); Proc. Roy.Soc.,A298, 184 (1967).

    Google Scholar 

  11. N.B.Backhouse, and P.Gard, J.Phys.A: Math.,Nucl.Gen., 7, 2101 (1974).

    Google Scholar 

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Authors and Affiliations

  1. Institut für Physikalische und Theoretische Chemie, Technical University, A-8010, Graz, Austria

    H. P. Fritzer

Authors
  1. H. P. Fritzer
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A. Janner T. Janssen M. Boon

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© 1976 Springer-Verlag

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Fritzer, H.P. (1976). A chemist looks at the structure of symmetry groups. In: Janner, A., Janssen, T., Boon, M. (eds) Group Theoretical Methods in Physics. Lecture Notes in Physics, vol 50. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-07789-8_35

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  • DOI: https://doi.org/10.1007/3-540-07789-8_35

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07789-3

  • Online ISBN: 978-3-540-38252-2

  • eBook Packages: Springer Book Archive

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