[GAP Forum] Generators
Petr Savicky
savicky at cs.cas.cz
Tue Apr 28 13:18:11 BST 2015
On Tue, Apr 28, 2015 at 10:10:46AM +0000, abdulhakeem alayiwola wrote:
> why does Gap list for example Dihedral group of order 8 as pc group of size
> 8 with 3 generators. when we know d8 has 2 generators?
The description of pc groups is contained in sections 45 and 46
of the reference
http://www.gap-system.org/Manuals/doc/ref/chap45.html#X86007B0083F60470
http://www.gap-system.org/Manuals/doc/ref/chap46.html#X7EAD57C97EBF7E67
In particular, Section 45.1 Polycyclic Generating Systems says
For many applications we have to assume that each of the relative
orders r_i is either a prime or infinity. This is equivalent to saying
that there are no trivial factors in the pc series and the finite
factors of the pc series are maximal refined.
The generators of pc group for d8 correspond to the three prime
factors of 8.
Hope this helps.
Petr Savicky.
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