This is just a question for fun:
As far as I know, frequently it is considered to be customary to denote an additive commutative group as 'abelian group' in lowercase, although the term is named after the mathematician Abel.
And also as far as I know the reason is:
Among mathematical adjectives derived from the proper name of a mathematician, the word "abelian" is rare in that it is often spelled with a lowercase a, rather than an uppercase A, indicating how ubiquitous the concept is in modern mathematics.
…as Wikipedia says.
But it seems quiet funny to me, since there are other many ubiquitous concepts throughout the whole mathematics that are named after many other mathematicians, but they are still spelled in uppercases (like 'Gaussian').
So my question is:
How did the term 'abelian' started to be spelled in this way? How was such custom absorbed to the mathematician society?
Are there other terms named after mathematicians that have custom of lowercase spelling in mathematics?
Maybe it more a social science question than a mathematics one, but it might be funny to know the root of the term that I have to use every day. :D
Traditionally, "Abelian" would be capitalized, as one finds, for instance, in the writings of Burnside and Ledermann.
In 1937, Emil Artin, who had a Jewish wife, had to leave Germany, and settled in the United States. He wrote the very influential Galois Theory in 1942, where "abelian" was used in lower case throughout the book. It is possible that Artin was unaware of the nuances in capitalization rules between German and English. It is also possible that his proof readers, if he had any, were unaware that "abelian" referred to a person.
Serge Lang credits Artin with teaching him algebra, and he followed his use of lower case "abelian" in his Algebra (1965). Birkhoff and Mac Lane also used lower case in their Algebra (1967). With such influential text books setting the pace, it was natural for later generations to follow up.