I'm not sure if Sage can always tell, if you multiply an element of a
subgroup by an element of the larger group, that the result should make
sense and lie in the larger group. You should be able to fix this by
forcing Sage to consider the subgroup element as lying in the larger group:
rather than
S4.subgroups()[19][1] * S4[1]
use
S4(S4.subgroups()[19][1]) * S4[1]
On Monday, January 29, 2018 at 3:20:16 PM UTC-8, Hsin-Po Wang wrote:
>
> The following code
>
> sage: S4=SymmetricGroup(*4*)
>
> sage: S4.subgroups()[*19*][*1*]*S4[*1*]
>
> raises an error
>
> TypeError: unsupported operand parent(s) for *: 'Subgroup of (Symmetric
> group of order 4! as a permutation group) generated by [(1,3)(2,4),
> (1,4,3,2)]' and 'Symmetric group of order 4! as a permutation group'
>
> I am not sure what exactly happened but this is quite peculiar. Among al
> 30 subgroups of S4 only the 19th and 27th raise errors.
>
> sage: *for* Sid,S in enumerate(S4.subgroups()):
>
> ....: *for* s in S:
>
> ....: *for* g in S4:
>
> ....: *try*:
>
> ....: sg=s*g
>
> ....: *except* *TypeError*:
>
> ....: #print'For {}-th subgroup: {}*{} is
> bad'.format(Sid,s,g)
>
> ....: *print* Sid,
>
> ....:
>
>
> 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19
> 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19
> 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19
> 19 19 19 19 19 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27
> 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27
> 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27
> 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27
> 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27
> 27 27 27 27 27 27 27 27
>
> I am using Sage 8.0.0 on macOS 10.13.2
>
>
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