Elements $Ain GL_4(mathbb{Z}_2)$ with $A^5=I, Aneq I$ by using GAP.
0
I need elements $Ain GL_4(mathbb{Z}_2)$(General linear group of $4times 4$ matrices over $mathbb{Z}_2$ ) with $A^5=I, Aneq I.$ By using simple calculation its hard to find such types of elements. So i think GAP or Magma is suitable for it. I am new in GAP. Please suggest me how to find this types of matrices with a suitable LoadPackage(if necessary). Thanks.
matrices group-theory gap magma
edited Dec 27 '18 at 9:31
Shaun
8,807113680
asked Dec 27 '18 at 4:11
neelkanth
2,0992928
|
show 4 more comments
0
I need elements $Ain GL_4(mathbb{Z}_2)$(General linear group of $4times 4$ matrices over $mathbb{Z}_2$ ) with $A^5=I, Aneq I.$ By using simple calculation its hard to find such types of elements. So i think GAP or Magma is suitable for it. I am new in GAP. Please suggest me how to find this types of matrices with a suitable LoadPackage(if necessary). Thanks.
matrices group-theory gap magma
edited Dec 27 '18 at 9:31
Shaun
8,807113680
asked Dec 27 '18 at 4:11
neelkanth
2,0992928
This is the same question as asking for subgroups of order $5$, which is a standard GAP call.
– Randall
Dec 27 '18 at 4:22
Yes it is same but i am new in GAP please if possible tell me a command ....thanks..
– neelkanth
Dec 27 '18 at 4:25
gap>g:=GL(4,2); then what command should i use ?
– neelkanth
Dec 27 '18 at 4:26
2
One can easily write down such matrices by hand: the companion matrix of $X^4+X^3+X^2+X+1$ and its conjugates.
– Lord Shark the Unknown
Dec 27 '18 at 5:54
2
There are 1344 such matrices. I suggest to look at the GAP Software Carpentry lesson - the 1st episode introduces all commands needed for doing that by a straightforward approach, and in some next episode you will see how one can useConjugacyClassesto deal with properties that are invariants of conjugacy classes more efficiently.
– Alexander Konovalov
Dec 27 '18 at 9:31
|
show 4 more comments
0
0
0
1
I need elements $Ain GL_4(mathbb{Z}_2)$(General linear group of $4times 4$ matrices over $mathbb{Z}_2$ ) with $A^5=I, Aneq I.$ By using simple calculation its hard to find such types of elements. So i think GAP or Magma is suitable for it. I am new in GAP. Please suggest me how to find this types of matrices with a suitable LoadPackage(if necessary). Thanks.
matrices group-theory gap magma
edited Dec 27 '18 at 9:31
Shaun
8,807113680
asked Dec 27 '18 at 4:11
neelkanth
2,0992928
I need elements $Ain GL_4(mathbb{Z}_2)$(General linear group of $4times 4$ matrices over $mathbb{Z}_2$ ) with $A^5=I, Aneq I.$ By using simple calculation its hard to find such types of elements. So i think GAP or Magma is suitable for it. I am new in GAP. Please suggest me how to find this types of matrices with a suitable LoadPackage(if necessary). Thanks.
matrices group-theory gap magma
matrices group-theory gap magma
edited Dec 27 '18 at 9:31
Shaun
8,807113680
asked Dec 27 '18 at 4:11
neelkanth
2,0992928
edited Dec 27 '18 at 9:31
Shaun
8,807113680
asked Dec 27 '18 at 4:11
neelkanth
2,0992928
edited Dec 27 '18 at 9:31
Shaun
8,807113680
edited Dec 27 '18 at 9:31
Shaun
8,807113680
edited Dec 27 '18 at 9:31
Shaun
8,807113680
8,807113680
asked Dec 27 '18 at 4:11
neelkanth
2,0992928
asked Dec 27 '18 at 4:11
neelkanth
2,0992928
asked Dec 27 '18 at 4:11
neelkanth
2,0992928
2,0992928
This is the same question as asking for subgroups of order $5$, which is a standard GAP call.
– Randall
Dec 27 '18 at 4:22
Yes it is same but i am new in GAP please if possible tell me a command ....thanks..
– neelkanth
Dec 27 '18 at 4:25
gap>g:=GL(4,2); then what command should i use ?
– neelkanth
Dec 27 '18 at 4:26
2
One can easily write down such matrices by hand: the companion matrix of $X^4+X^3+X^2+X+1$ and its conjugates.
– Lord Shark the Unknown
Dec 27 '18 at 5:54
2
There are 1344 such matrices. I suggest to look at the GAP Software Carpentry lesson - the 1st episode introduces all commands needed for doing that by a straightforward approach, and in some next episode you will see how one can useConjugacyClassesto deal with properties that are invariants of conjugacy classes more efficiently.
– Alexander Konovalov
Dec 27 '18 at 9:31
|
show 4 more comments
This is the same question as asking for subgroups of order $5$, which is a standard GAP call.
– Randall
Dec 27 '18 at 4:22
Yes it is same but i am new in GAP please if possible tell me a command ....thanks..
– neelkanth
Dec 27 '18 at 4:25
gap>g:=GL(4,2); then what command should i use ?
– neelkanth
Dec 27 '18 at 4:26
2
One can easily write down such matrices by hand: the companion matrix of $X^4+X^3+X^2+X+1$ and its conjugates.
– Lord Shark the Unknown
Dec 27 '18 at 5:54
2
There are 1344 such matrices. I suggest to look at the GAP Software Carpentry lesson - the 1st episode introduces all commands needed for doing that by a straightforward approach, and in some next episode you will see how one can useConjugacyClassesto deal with properties that are invariants of conjugacy classes more efficiently.
– Alexander Konovalov
Dec 27 '18 at 9:31
This is the same question as asking for subgroups of order $5$, which is a standard GAP call.
– Randall
Dec 27 '18 at 4:22
This is the same question as asking for subgroups of order $5$, which is a standard GAP call.
– Randall
Dec 27 '18 at 4:22
Yes it is same but i am new in GAP please if possible tell me a command ....thanks..
– neelkanth
Dec 27 '18 at 4:25
Yes it is same but i am new in GAP please if possible tell me a command ....thanks..
– neelkanth
Dec 27 '18 at 4:25
gap>g:=GL(4,2); then what command should i use ?
– neelkanth
Dec 27 '18 at 4:26
gap>g:=GL(4,2); then what command should i use ?
– neelkanth
Dec 27 '18 at 4:26
2
2
One can easily write down such matrices by hand: the companion matrix of $X^4+X^3+X^2+X+1$ and its conjugates.
– Lord Shark the Unknown
Dec 27 '18 at 5:54
One can easily write down such matrices by hand: the companion matrix of $X^4+X^3+X^2+X+1$ and its conjugates.
– Lord Shark the Unknown
Dec 27 '18 at 5:54
2
2
There are 1344 such matrices. I suggest to look at the GAP Software Carpentry lesson - the 1st episode introduces all commands needed for doing that by a straightforward approach, and in some next episode you will see how one can use
ConjugacyClasses to deal with properties that are invariants of conjugacy classes more efficiently.– Alexander Konovalov
Dec 27 '18 at 9:31
There are 1344 such matrices. I suggest to look at the GAP Software Carpentry lesson - the 1st episode introduces all commands needed for doing that by a straightforward approach, and in some next episode you will see how one can use
ConjugacyClasses to deal with properties that are invariants of conjugacy classes more efficiently.– Alexander Konovalov
Dec 27 '18 at 9:31
|
show 4 more comments
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This is the same question as asking for subgroups of order $5$, which is a standard GAP call.
– Randall
Dec 27 '18 at 4:22
Yes it is same but i am new in GAP please if possible tell me a command ....thanks..
– neelkanth
Dec 27 '18 at 4:25
gap>g:=GL(4,2); then what command should i use ?
– neelkanth
Dec 27 '18 at 4:26
2
One can easily write down such matrices by hand: the companion matrix of $X^4+X^3+X^2+X+1$ and its conjugates.
– Lord Shark the Unknown
Dec 27 '18 at 5:54
2
There are 1344 such matrices. I suggest to look at the GAP Software Carpentry lesson - the 1st episode introduces all commands needed for doing that by a straightforward approach, and in some next episode you will see how one can use
ConjugacyClassesto deal with properties that are invariants of conjugacy classes more efficiently.– Alexander Konovalov
Dec 27 '18 at 9:31