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

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==Definition==
 
==Definition==
  
This [[group]] is defined as the [[general linear group of degree three]] over [[field:F3]].
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This [[group]] is defined in the following equivalent ways:
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# It is the [[member of family::general linear group]] of [[member of family::general linear group of degree three|degree three]] over [[field:F3]].
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# It is the [[external direct product]] of [[projective special linear group:PSL(3,3)]] and [[cyclic group:Z2]].
  
 
==Arithmetic functions==
 
==Arithmetic functions==
  
 
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! Function !! Value !! Explanation
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! Function !! Value !! Similar groups !! 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 given order|exponent of a group|312|11232}} ||
 
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==GAP implementation===
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==GAP implementation==
  
 
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Latest revision as of 02:55, 2 November 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
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Definition

This group is defined in the following equivalent ways:

  1. It is the general linear group of degree three over field:F3.
  2. It is the external direct product of projective special linear group:PSL(3,3) and cyclic group:Z2.

Arithmetic functions

Function Value Similar groups Explanation
order (number of elements, equivalently, cardinality or size of underlying set) 11232 groups with same order order 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
exponent of a group 312 groups with same order and exponent of a group | groups with same exponent of a group

GAP implementation

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