# Element structure of special linear group:SL(2,Q)

From Groupprops

This article gives specific information, namely, element structure, about a particular group, namely: special linear group:SL(2,Q).

View element structure of particular groups | View other specific information about special linear group:SL(2,Q)

This article aims to discuss the element structure of special linear group:SL(2,Q), i.e., the special linear group of degree two over the field of rational numbers.

## Related information

- Element structure of special linear group of degree two over a field: This is very general, but requres a large number of cases and takes a lot of effort to understand in its entirety.
- Element structure of special linear group of degree two over a finite field

## Conjugacy class structure

The conjugacy class structure basically follows from Element structure of special linear group of degree two over a field and a number of computations specific to the rational numbers. Unfortunately, some of the actual descriptions of how conjugacy classes split relative to general linear group:GL(2,Q) requires deep (and may be open?) facts from number theory. However, we*can*fill in the broad outlines.

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