[GAP Forum] linear groups over ZmodnZ(p^k)

[Vincent Delecroix]

Dear all,

My aim is to perform computations with linear groups over Z / p^k Z
(actually over p-adics). Something like Sp(6, ZmodnZ(4)) would be a good
first example and Sp(6, ZmodnZ(16)) a more realistic one. Is there
already something available that I wouldn't have noticed?

My first computation was the Size. In the case k=1, everything is set
upon construction and hence works fine. But for k > 1, the computation
never ends. Though the cardinality is not complicated to compute (using
reduction mod p).

Two concrete question

* if I have a function SizeSpZmodnZ, is there a way to tell GAP to use
   it when I call Size(Sp(6, ZmodnZ(8))?

* I might just program a more general SizeLinearGroupZmodnZ which
   would just go through the same algorithm. What should I do to
   properly apply the previous step to all linear groups?

This message is from the joint meeting https://wiki.sagemath.org/days93 
where we are sadly lacking GAP expertise...

Best
Vincent