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

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(Arithmetic functions)
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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>
 
| {{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|11232|312}}
 
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==GAP implementation===
 
==GAP implementation===
  

Revision as of 02:51, 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
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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
exponent of a group 11232 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