1. Making a or passage.
  2. Affected by of signification.
  3. Taking an or objects.
    The English verb "to notice" is a transitive verb, because we say things like "She noticed a problem".
  4. Having the property that if an element x is related to y and y is related to z, then x is necessarily related to z.
    "Is an ancestor of" is a transitive relation: if Alice is an ancestor of Bob, and Bob is an ancestor of Carol, then Alice is an ancestor of Carol.
  5. Such that, for any two elements of the acted-upon set, some group element maps the first to the second.

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