Article ID: CBB001212298

What's Abelian about Abelian Groups? (2013)

unapi

The association of names to mathematical concepts and results (the creation of eponyms) is often a curious process. For the case of abelian groups, we will be taken on a quick, guided tour of the life of Niels Henrik Abel, elliptic functions, a curve called the lemniscate, the construction of the regular 17-gon, and a particular class of solvable equations before we can begin to appreciate how Abel's name was attributed to a concept (groups) not yet invented in his lifetime. Therefore, I will have to address how `group theory' was done before it was even invented. As the story unfolds, indications of a broader development in mathematics in the early nineteenth century will emerge. In that century, large parts of analysis underwent transformations from a predominantly formula-centred approach to a more conceptual one, and our story features important examples of how the processes of generalization functioned.

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Authors & Contributors
Hollings, Christopher David
Ehrhardt, Caroline
Sørensen, Henrik Kragh
Rosen, Michael I.
Piene, Ragni
Parshall, Karen V. Hunger
Concepts
Mathematics
Algebra
Mathematicians
Group theory
Algebraic geometry
Functions (mathematics)
Time Periods
19th century
20th century, early
20th century
21st century
18th century
Places
France
China
England
Ukraine
Scotland
Russia
Institutions
Imperial University of Peking
University of Chicago
Académie des Sciences, Paris
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