Burnside base set

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The basic set of Burnside is a result of the group theory . It says that in a finite p-group all non-shortenable generating systems contain the same number of elements. The number d of elements in a generating system that cannot be shortened is the dimension of the factor group after the Frattini group . Since this group of factors is elementary, it can be regarded as a vector space over the body with p elements and therefore has a dimension d as a vector space; their cardinality is then equal to p d . Burnside's basic theorem also states that every group element that is not in the Frattini group is contained in a system of generators that cannot be shortened.

literature

  • Bertram Huppert: Finite Groups I. Springer-Verlag, Berlin a. a. 1979. ISBN 3-540-03825-6 . Cape. III, par. 3, sentence 3.15, page 273.