Fix FactorCosetAction(G, G) for perm. groups

[ThomasBreuer]

Catch the case of an action with trivial image in DoFactorCosetActionPerm, and delegate to DoFactorCosetAction in this case.

resolves #5902

(Just for curiosity:
The code for DoFactorCosetAction and DoFactorCosetActionPerm deals with the case that the second argument is a list (not a group), but only in order to call Error if this list is empty. The functions called later, such as Core and ActionRefinedSeries, do not accept a list as the value of this argument.
Is this list situation meaningful at all?)

[ThomasBreuer]

I do not understand the remark that the added lines are not covered by tests.
The added test in teststandard should execute these lines of code, I have checked this locally.
What am I missing?

[lgoettgens]

I do not understand the remark that the added lines are not covered by tests. The added test in teststandard should execute these lines of code, I have checked this locally. What am I missing?

If we have a look at the codecov webpage (https://app.codecov.io/gh/gap-system/gap/pull/5903/blob/lib/csetperm.gi#L886), it there states that your added lines are indeed covered (aka are green), while the error case two lines above is uncovered. My assumption is that there is a small offset somewhere in the codecov-to-github interface that mistakenly reports this

[fingolfin]

Backported to stable-4.14 in fb105c9

[mantepse]

Please excuse me for commenting under a closed issue - I'm not sure whether I should open a new one or ask on the mailing list first, please let me know.

I think I found an example where the issue still occurfor the following question:

(Just for curiosity: The code for DoFactorCosetAction and DoFactorCosetActionPerm deals with the case that the second argument is a list (not a group), but only in order to call Error if this list is empty. The functions called later, such as Core and ActionRefinedSeries, do not accept a list as the value of this argument. Is this list situation meaningful at all?)

I have code (in sagemath, sagemath/sage#40186) that produces such a situation - although I am not sure whether or not I might be abusing FactorCosetAction. More precisely, I have a list of stabilizer subgroups of a symmetric group, and I want to create the corresponding action. In the trivial case, this fails:

gap> S := SymmetricGroup(1);
Group(())

gap> FactorCosetAction(S, S);
<action epimorphism>

gap> FactorCosetAction(S, [S]);
Error, usage: Group(<gen>,...), Group(<gens>), Group(<gens>,<id>) at /home/martin/sage/local/share/gap/lib/grp.gi:4989 called from
Group( d ) at /home/martin/sage/local/share/gap/lib/factgrp.gi:555 called from
<function "FactorCosetAction On cosets of list of groups">( <arguments> )
 called from read-eval loop at *stdin*:15
you can 'quit;' to quit to outer loop, or
you can 'return;' to continue
brk> quit;

gap> FactorCosetAction(S, [S, S]);
Error, usage: Group(<gen>,...), Group(<gens>), Group(<gens>,<id>) at /home/martin/sage/local/share/gap/lib/grp.gi:4989 called from
Group( d ) at /home/martin/sage/local/share/gap/lib/factgrp.gi:555 called from
<function "FactorCosetAction On cosets of list of groups">( <arguments> )
 called from read-eval loop at *stdin*:15
you can 'quit;' to quit to outer loop, or
you can 'return;' to continue

Apparantly, this only happens for the trivial group:

gap> S := SymmetricGroup(2);
Sym( [ 1 .. 2 ] )

gap> FactorCosetAction(S, S);
<action epimorphism>

gap> FactorCosetAction(S, [S]);
[ (1,2) ] -> [ () ]

gap> FactorCosetAction(S, [S, S]);
[ (1,2) ] -> [ () ]

[hulpke]

@mantepse Yes, if there is a chance that this operation gets called for the trivial group, this case (which will always just map to the trivial permutation group on 0 points), one needs to catch it at the start. (One of the tricksy bits is that the group on 1 point acts actually on 0.)

The list functionality is definitive needed -- it is used to construct (subdirectories product) permutation actions on the cosets of multiple subgroups.