[GAP Forum] I am puzzled by the function DihedralGroup(n)!

[Laurent Bartholdi]

Very simple: groups are sometimes presented with minimal generating
set, sometimes not. (D_{2n} could also be given by 2n generators; this
would be very inefficient).
In this case, the groups are finite pc-groups, which means they have a
series of subgroups such that the successive quotients are cyclic of
prime order. There is one generator per quotient. (try n=12, 14, 16,
18 to see!)

If you really need a 2-element generating set, you may consider either
'MinimalGeneratingSet(DihedralGroup(2*n))';
or construct initially the group by 'DihedralGroup(IsPermGroup,2*n)',
which gives a permutation group with 2 generators.

A question for the GAP people: shouldn't there be a method for
'DihedralGroup(IsFpGroup,2*n)'?

On Nov 27, 2007 3:15 AM, ¶­¾®³É <dongjc at njau.edu.cn> wrote:
> Dear Forum,Dear Everyone:
> As we all know, a dihedral group  $D_{2n}$ is generated by two elements $a$ and $b$ such that $a^n=1,b^2=1$ and $aba=b$. Hence $D_{2n}$ consists of  $2n$ elements. However the following statements puzzle me:
> gap>d8:=DihedralGroup(8);
> <pc group of size 8 with 3 generators>
> gap>d10:=DihedralGroup(10);
> <pc group of size 10 with 2 generators>
> The first statement implies that d8 has 3 generators. The second statement implies that d10 has 2 elements. WHY?
> Best wishes!
>
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