= Degree
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The degree of some <algebraic structure> is some parameter that describes the structure. There is no universal definition valid for all structures, it is a per structure type thing.
This is particularly useful when talking about structures with an <infinite> number of elements, but it is sometimes also used for finite structures.
Examples:
* the <dihedral group> of degree n acts on n elements, and has order 2n
* the parameter $n$ that characterizes the size of the <general linear group> $GL(n)$ is called the degree of that group, i.e. the dimension of the underlying matrices