Divisible Group - Properties

Properties

  • If a divisible group is a subgroup of an abelian group then it is a direct summand.
  • Every abelian group can be embedded in a divisible group.
  • Non-trivial divisible groups are not finitely generated.
  • Further, every abelian group can be embedded in a divisible group as an essential subgroup in a unique way.
  • An abelian group is divisible if and only if it is p-divisible for every prime p.
  • Let be a ring. If is a divisible group, then is injective in the category of -modules.

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