Space Groups, Brillouin Zone and the Group of k

  • Richard L. Liboff
Part of the Undergraduate Texts in Contemporary Physics book series (UTCP)


Consider that a finite group G has the subgroup S. We recall that the order of S divides the order of G, so that g/s = n, where n is an integer and g and s are the orders of G and S, respectively (Section 1.4). Let p be an element of G but not of S, so that pG - S (Fig. 5.1).


Brillouin Zone Point Group Factor Group Reciprocal Lattice Translation Vector 
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  1. 1.
    The factor group was introduced by E’variste Galois (1811–1832). See Chapter 7.Google Scholar
  2. 2.
    For further discussion, see J.F. Cornwell, Group Theory in Physics (see Bibliography).Google Scholar
  3. 3.
    This scheme is described in N.F. Henry and K. Lonsdale; G. Burns (see Bibliography).Google Scholar

Copyright information

© Springer-Verlag New York, Inc. 2004

Authors and Affiliations

  • Richard L. Liboff
    • 1
  1. 1.School of Electrical EngineeringCornell UniversityIthacaUSA

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