what does this notation mean:
$(\chi(D),p^j)$
where $\chi(D)$ - character of the group ring. D - element of the group of ring, p - prime number.
It is looks like a greatest common divisor, but it is not.
I found this notation in the book Addition theorems, H. B. MANN, 1965.
https://www.amazon.com/Addition-Theorems-H-B-Mann/dp/047056735X
without explanation:
I am sorry, but the comment of David A. Craven help me to understand that it is in fact the greatest common divisor but in algebraic number field.
In fact, if we accept that this is a GCD, then the proof of the theorem will be true, as can be seen in the attached screenshot.
The prime number decomposition in algebraic number field confused me a little, so I did not immediately understand this notation.