# Difference between revisions of "Special linear group:SL(2,Z)"

From Groupprops

(Created page with '{{particular group}} ==Definition== The group <math>SL(2,\mathbb{Z})</math> is defined as the group, under matrix multiplication, of <math>2 \times 2</math> matrices over <math…') |
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In other words, it is the group with underlying set: | In other words, it is the group with underlying set: | ||

− | <math>\{ \begin{pmatrix} a & b \\ c & d \\\end{pmatrix} \mid a,b,c,d \in \mathbb{Z}, ad - bc = 1 \}</math> | + | <math>\left \{ \begin{pmatrix} a & b \\ c & d \\\end{pmatrix} \mid a,b,c,d \in \mathbb{Z}, ad - bc = 1 \right \}</math> |

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+ | This is the degree two case of a [[member of family::special linear group over integers]] and hence of a [[member of family::special linear group]]. | ||

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+ | ==GAP implementation== | ||

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+ | The group can be defined as: | ||

+ | |||

+ | <pre>SL(2,Integers)</pre> |

## Revision as of 21:42, 24 August 2009

This article is about a particular group, i.e., a group unique upto isomorphism. View specific information (such as linear representation theory, subgroup structure) about this groupView a complete list of particular groups (this is a very huge list!)[SHOW MORE]

## Definition

The group is defined as the group, under matrix multiplication, of matrices over , the ring of integers, having determinant .

In other words, it is the group with underlying set:

This is the degree two case of a special linear group over integers and hence of a special linear group.

## GAP implementation

The group can be defined as:

SL(2,Integers)