Difference between revisions of "General linear group:GL(3,3)"

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(Created page with "{{particular group}} ==Definition== This group is defined as the general linear group of degree three over field:F3. ==Arithmetic functions== {| class="sortable" ...")
 
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! Function !! Value !! Explanation
 
! Function !! Value !! Explanation
 
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| {{arithmetic function value order|11232}} || order of a [[general linear group of degree three]] over a [[finite field]] with <math>q</math> elements is <math>(q^3 - 1)(q^3 - q)(q^3 - q^2)</math>. For <math>q = 3</math>, we get <math>(26)(24)(18) = 11232</math>
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| {{arithmetic function value order|11232}}order of a [[general linear group of degree three]] over a [[finite field]] with <math>q</math> elements is <math>(q^3 - 1)(q^3 - q)(q^3 - q^2)</math>. For <math>q = 3</math>, we get <math>(26)(24)(18) = 11232</math>
 
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| {{arithmetic function value exponent|312}} ||
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| {{arithmetic function value exponent|312}}
 
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==GAP implementation===
 
==GAP implementation===

Revision as of 02:50, 31 October 2010

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 group
View a complete list of particular groups (this is a very huge list!)[SHOW MORE]

Definition

This group is defined as the general linear group of degree three over field:F3.

Arithmetic functions

Function Value Explanation
order (number of elements, equivalently, cardinality or size of underlying set) 11232 groups with same orderorder of a general linear group of degree three over a finite field with q elements is (q^3 - 1)(q^3 - q)(q^3 - q^2). For q = 3, we get (26)(24)(18) = 11232
Template:Arithmetic function value exponent

GAP implementation=

Description Functions used
GL(3,3) or GeneralLinearGroup(3,3) GAP:GL