Making the world better, one answer at a time. Genitive is a grammatical case indicating that a thing belongs to another. A saxon genitive is one which is formed with an apostrophe 's' to denote ownership.For example, 'the man's dog', meaning the dog of the man.aking the world better, one answer at a time. Genitive is a grammatical case indicating that a thing belongs to another. A saxon genitive is one which is formed with an apostrophe 's' to denote ownership.