Learn English – Possessive of plural nouns

1. We speak of possessive or genitive only when a noun (or noun phrase) is marked with the 's clitic (or with a bare apostrophe if the noun or noun phrase ends with ‹s› or ‹z›).

   None of your examples employs this marker, so all of them are what grammarians call attributive nouns: nouns which act like adjectives 'modifying' a following noun.

   (Some writers on grammar also call constructions with of preposition phrases, like NOUN of NOUN, 'genitive'; but that is not relevant here.)

2. The term possessive is a grammatical term, not a semantic one—that is, not a term which indicates actual "possession". There are other relationships which the possessive may signify. For instance, when the second noun, the one which is not possessive, is derived from a verb, the noun in the possessive case may be the agent, the semantic subject of the action which the second noun designates:

   Columbus' discovery of America ← Columbus discovered America

   In other cases the possessive may mark the patient, the semantic object of the action:

   Germany's defeat by the Allies → Germany was defeated by the Allies

3. Attributive nouns have an even wider range of reference. A bicycle rider is someone who rides a bicycle, a bicycle store is a store where bicycles are sold, a bicycle tire is a tire for a bicycle, a bicycle race is a race in which the competitors ride bicycles. In your examples:

   • Syllabus highlights are the main points in a syllabus
   • Relationship problems are problems with or concerning a relationship
   • Admission requirements are what is required of those who apply for admission

As noted in comments, it's generally (unofficially) discouraged to use "women" or "woman" as an adjective. It's preferred to use "female".

So, while these may be perfectly fine, they are not adjectival uses of "woman":

The woman pilots the plane.
At Airline X, women pilot all of the planes.
_{*Note that in these examples, "pilot" is a verb, not a noun.}

The preferred use would be:

Female pilots were well known as early as the 1960s.

As a note, none of these uses are "possessives". There's no show of ownership at all. It's just describing the type of pilot you're talking about.

This section options 1 and 4 both use the possessive but 2 and 3 do not:

1. Women's jobs
2. Women jobs
3. Woman jobs
4. Woman's jobs.

So, if your goal is to understand the possessive use, I'll ignore 2 and 3, which I don't think should ever be used, regardless of possession.

Version 1 is plural possessive. If that's what you're looking for, this is your choice. "Women" is plural and the "apostrophe s" makes it possessive.

Version 4 is singular possessive. "Woman" is singular and the "apostrophe s" makes it possessive.