I have been self studying Apostol Introduction to analytic number theory and I have a doubt in text of Chapter 6 of the book .
Apostol mentions in section 6.5 ( Characters of finite Abelian Groups)
Every group G has at least one character, namely the function which is identically 1 on G. This is called principal character .
My doubt is how to prove existence of such a function on every finite group ie how to prove such a character definitely exists for every finite group.
Can anyone please give explanation for this