Ciro Santilli @cirosantilli 34

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:

Forms a normal subgroup of the general linear group.

general linear group over a finite field of order $m$. Remember that due to the classification of finite fields, there is one single field for each prime power $m$.

Exactly as over the real numbers, you just put the finite field elements into a $n\times n$ matrix, and then take the invertible ones.

The set of all invertible matrices forms a group: the general linear group with matrix multiplication. Non-invertible matrices don't form a group due to the lack of inverse.

The author seems to have uploaded the entire book by chapters at: www.physics.drexel.edu/~bob/LieGroups.html

And the author is the cutest: www.physics.drexel.edu/~bob/Personal.html.

Overview:

Forms a normal subgroup of the general linear group.

Specials sub case of the general linear group when the determinant equals exactly 1.