This is a question specifically about English language usage in mathematics, but it is probably the same in all topics (however I can't really think of an example in everyday life!).
Should I say "A is conjugate to B" or "A is conjugate with B"? I'm pretty sure "A is the conjugate of B" is acceptable, but I think (at least one) of the previous is also correct.
I'm referring to "conjugate" as in "subgroups are conjugate".
Best Answer
As per Wikipedia on algebraic conjugates, it would be correct to say, "A is the conjugate of B," as you have noted. And of course, B is the conjugate of A, given that conjugates come in pairs.
Based on my experience, it would also be correct to say, "A is conjugate to B," with the reverse also being true. No mathematician's eyebrows would go up.
On the other hand, I don't know anyone who deals with these issues on a regular basis who would say, "A is conjugate with B." Instead, they would say, "A and B are conjugates," as suggested by @PhilSweet. I admit that this is on the soft side for ELU, but that's just the way it is.