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In English I would say: "Let G be a locally compact group."

In French I think it would go something like: "Soit G être d'un groupe localement compact."

But I don't think I have conjugated the verb être properly.

Can someone correct me?


Update: I found an example of this in literature, appearing as: “Soit G un groupe localement compact.”

So does the phrase “Soit G …” mean something along the lines of “Let G be that which is …”?

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1 Answer 1

up vote 7 down vote accepted

Actually, “soit” is the subjonctif présent 3rd person singular of “être”.

The correct form is indeed:

Soit G un groupe localement compact […]

When the subject is plural, e.g. “Let G and H be locally compact groups”, you can use either “Soient” (subjonctif présent, 3rd person plural) or “Soit”, as the construction became idiomatic.

Soient G et H des groupes localement compacts […]

Soit G et H des groupes localement compacts […]

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So you have to pluralize 'compacts' to match up with the pluralization of 'groupes'? –  Kyle Schlitt May 4 at 23:11
2  
Yes, as with every adjective in French. –  Édouard May 5 at 0:59

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