Editing Group theory (section)

===Algebraic number theory===
{{Main|Algebraic number theory}}
[[Algebraic number theory]] makes uses of groups for some important applications. For example, [[Euler product|Euler's product formula]],
:<math>
\begin{align}
\sum_{n\geq 1}\frac{1}{n^s}& = \prod_{p \text{ prime}} \frac{1}{1-p^{-s}}, \\
\end{align}
\!</math>
captures [[Fundamental theorem of arithmetic|the fact]] that any integer decomposes in a unique way into [[prime number|primes]]. The failure of this statement for [[Dedekind ring|more general rings]] gives rise to [[class group]]s and [[regular prime]]s, which feature in [[Ernst Kummer|Kummer's]] treatment of [[Fermat's Last Theorem]].