# Element structure of special linear group of degree two over a finite discrete valuation ring

From Groupprops

## Contents |

This article gives specific information, namely, element structure, about a family of groups, namely: special linear group of degree two.

View element structure of group families | View other specific information about special linear group of degree two

This article discusses the element structure of the special linear group of degree two over a finite discrete valuation ring (i.e., local principal ideal ring) with residue field having size , underlying prime characteristic of residue field , and length . The size of the whole ring is , and each successive power of the unique maximal ideal has index in its predecessor.

Examples are (here ), , and Galois rings.

The Galois ring with residue field of size and length is the unique (up to isomorphism) discrete valuation ring obtained as a degree extension of , and hence generalizes both and . The Galois ring has characteristic .

## Summary

Item | Value |
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order of the group | . |