For X a Y, something is true

Question

Often in mathematical writing I read (and write) constructions such as

For G a finite group, the character algebra is defined as ...

For X and Y sets, a function from X to Y is ...

The general structure here is

For NAME a TYPE, SOMETHING is true

i.e. we give something of a certain type a name, and then state some property or definition.

I'm not a native speaker, so I'm wondering if these constructions are correct in standard English, or if it is simply a product of a lot of non-native speakers contributing to science, and adding their own language's quirks into their writing.

My questions: Does it have a name? Is it formally/grammatically correct?

Answer 1

The structure can be explained:

• For G a finite group, the character algebra is defined as ...

is essentially a variant of

• For any finite group G, the character algebra is defined as ...

and can be considered a deleted form of

• For the situation where G is a finite group, the character algebra is defined as ...

................ Similarly,

For the situation where X and Y are [suitable] sets, a function from X to Y is ...

Mathspeak is preferred to the perhaps rather unprofessional-sounding spelled-out versions.

The 'suitable' is pragmatic, to pre-empt the arranging of silly, arbitrary (though 'legitimate' from other considerations) mappings. People's shoe sizes mapping to their favourite pets.