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. This article restricts attention to the case where the underlying ring is a finite discrete valuation ring.
View element structure of group families | View other specific information about special linear group of degree two | View other specific information about group families for rings of the type finite discrete valuation ring
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 |
---|---|
order of the group | . |
number of conjugacy classes | Case odd: , which is Case a power of 2: PLACEHOLDER FOR INFORMATION TO BE FILLED IN: [SHOW MORE] |