Divisible Group - Examples

Examples

  • The rational numbers form a divisible group under addition.
  • More generally, the underlying additive group of any vector space over is divisible.
  • Every quotient of a divisible group is divisible. Thus, is divisible.
  • The p-primary component of, which is isomorphic to the p-quasicyclic group is divisible.
  • Every existentially closed group (in the model theoretic sense) is divisible.
  • The space of orientation-preserving isometries of is divisible. This is because each such isometry is either a translation or a rotation about a point, and in either case the ability to "divide by n" is plainly present. This is the simplest example of a non-Abelian divisible group.

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