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user717
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Presentation(Non-trivial) presentation of general linear and symplectic group over Z/mZ?

I know that there exists a nice presentation (generators and relations) of the general linear group over a finite field (by Steinberg, I think). Is there also a nice presentation of $GL(n,\mathbb{Z}/m\mathbb{Z})$ for an arbitrary integer $m$? And perhaps also for the symplectic group over $\mathbb{Z}/m\mathbb{Z}$?

I want to do some calculations in these groups with a computer and my first problem was surprised thatto determine these groups. One solution $GL(n,\mathbb{Z}/m\mathbb{Z})$(my current) is implemented in GAPof course to determine both by brute force. But already for small m, so I assume that there exists a presentation but I could not find anything in the referencesn this takes too much time.

Presentation of general linear and symplectic group over Z/mZ?

I know that there exists a presentation (generators and relations) of the general linear group over a finite field. Is there also a presentation of $GL(n,\mathbb{Z}/m\mathbb{Z})$ for an arbitrary integer $m$? And perhaps also for the symplectic group over $\mathbb{Z}/m\mathbb{Z}$?

I was surprised that $GL(n,\mathbb{Z}/m\mathbb{Z})$ is implemented in GAP, so I assume that there exists a presentation but I could not find anything in the references.

(Non-trivial) presentation of general linear and symplectic group over Z/mZ?

I know that there exists a nice presentation (generators and relations) of the general linear group over a finite field (by Steinberg, I think). Is there also a nice presentation of $GL(n,\mathbb{Z}/m\mathbb{Z})$ for an arbitrary integer $m$? And perhaps also for the symplectic group over $\mathbb{Z}/m\mathbb{Z}$?

I want to do some calculations in these groups with a computer and my first problem was to determine these groups. One solution (my current) is of course to determine both by brute force. But already for small m,n this takes too much time.

Source Link
user717
  • 5.2k
  • 2
  • 38
  • 41

Presentation of general linear and symplectic group over Z/mZ?

I know that there exists a presentation (generators and relations) of the general linear group over a finite field. Is there also a presentation of $GL(n,\mathbb{Z}/m\mathbb{Z})$ for an arbitrary integer $m$? And perhaps also for the symplectic group over $\mathbb{Z}/m\mathbb{Z}$?

I was surprised that $GL(n,\mathbb{Z}/m\mathbb{Z})$ is implemented in GAP, so I assume that there exists a presentation but I could not find anything in the references.