[GAP Forum] Finding [2,p]-generated groups

R. Keith Dennis dennis at rkd.math.cornell.edu
Fri Jun 15 15:44:27 BST 2007


I'm doing similar, but more complicated computations now.  In your
case you can eliminate many groups from consideration almost instantly
by using EulerianFunction(G,2) to determine if the group is generated
by 2 elements or not.  After that, I suppose you could save a bit
by letting the first element range over representatives of conjugacy
classes of elements of order 2 (resp p), but for the second element
testing all relevant ones seems like the simplest way to go.  
I guess it depends on how many cases you want to check.

Keith

> I have the following problem: I want to list all the groups of order
>n generated by one element of order 2 and one element of order p>2,
>with p prime (and n divided by 2 and by p, of course). I can achieve
>that goal using the SmallGroup library and testing all the groups of
>order n, but is there any faster way ?  Same question for the groups
>generated by two elements of order p, with p prime.



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