On Tue, 2007-11-27 at 10:15 +0800, 董井成 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?
the 1st statement just says that this concrete representation has 3
generators. It does not contradict anything. There are many possible
representations...
HTH,
Dmitrii
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