I see many times the words "conjugacy" and "conjugation", and I don't really get the difference between the two. Especially, when we take an element of a group and want to say that this has some property "up to conjugacy/tion", which one is better, and why?



What is the difference between "up to conjugacy" and "up to conjugation" ?
To expand upon Gerhard's comment, I would add the following:


In English, the -acy suffix tends to denote the nounification of an *adjective* and the -ation suffix tends to denote the nounification of a *verb*. 


Obviously, 'conjugate' can act as both an adjective and a verb e.g. 
'$x$ and $y$ are conjugate' or 'One may conjugate $x$ by some element to get $y$'


Since these phrases are mathematically the same, there is thus no mathematical difference between '$x$ and $y$ are equal up to conjugacy' and '$x$ and $y$ are equal up to conjugation' 


