nLab
maximal central extension

Contents

Idea

Given some algebraic object like an associative algebra or group or Lie algebra which with a notion of central extension, one may ask for the largest possible such, the maximal central extension. This makes sense if one considers subobjects of a given algebraic object.

References

  • Katsuya Miyake, Hans Opolka, On nilpotent extensions of algebraic number fields I, Nagayo Math. J., Vol. 125 (1991), 1-14 (Euclid:1118783087)

The lower central series of the absolute Galois group of a field is obtained by iterating the process of forming the maximal central extension of the maximal nilpotent extension of a given class, starting with the maximal abelian extension. The purpose of this paper is to give a cohomological description of this central series in case of an algebraic number field.

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