The 'abelian group' custom

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 learning 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.