[GAP Forum] Order of elements in a group and their statistics
Stefanos Aivazidis
stefanosaivazidis at gmail.com
Fri Jul 12 22:58:55 BST 2013
Dear forum,
I have the following (rather naive) question to ask: what is the
most efficient way to find the spectrum of a finite group G, and
compute for each integer in the spectrum the number of elements with
given order? An integer d lies in the spectrum of G iff there exists
at least one g in G such that o(g)=d. The algorithm, I imagine, should
proceed along these lines:
1) define the group G,
2) compute the set of divisors of |G| and store this as a list L,
3) refine L (by excluding those divisors of |G| which do not
appear as element orders) to obtain the spectrum of G and
store this in a new list L',
4) compute how many elements of G have order d, for each d in L'
Your thoughts on how to make this precise algorithmically would
be much appreciated. Also, is it possible to produce a graph with
the statistics found by the main programme?
Many thanks in advance.
Best wishes,
Stefanos
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