SemidirectProduct error if group has no generators

[ignatsoroko]

Observed behaviour

gap> G:=SymmetricGroup(3);;
gap> H:=SubgroupProperty(G,x->Order(x)=1);
Group(())
gap> T:=Group(());
Group(())
gap> H=T;
true
gap> GeneratorsOfGroup(H);
[  ]
gap> GeneratorsOfGroup(T);
[ () ]
gap> T=Group(GeneratorsOfGroup(T));
true
gap> H=Group(GeneratorsOfGroup(H));
Error, usage: Group(<gen>,...), Group(<gens>), Group(<gens>,<id>) at /proc/cygdrive/C/gap-4.10.0-x86_64/lib/grp.gi:4563 called from
<function "Group">( <arguments> )
 called from read-eval loop at *stdin*:9
you can 'quit;' to quit to outer loop, or
you can 'return;' to continue
brk> quit;

Expected behaviour

gap> H=Group(GeneratorsOfGroup(H));
true

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[ChrisJefferson]

This is related to some previous issues ,for example #1239

The fix for this is to pass the identity as the optional second argument of group, say Group(GeneratorsOfGroup(H, () ), or in general Group(GeneratorsOfGroup(H), Identity(H)).

[hulpke]

Just to add to @ChrisJefferson's remark: If the generator list is (potentially) empty, the identity needs to be given, as GAP otherwise has no way of finding out what it would be (identity permutation, matrix, idword, ...)

I suggest we close this.

[ignatsoroko]

I am sorry to bring up this semi-trivial issue, but there are situations where it does cause error. For instance, continuing with the example above,

gap> A:=AutomorphismGroup(H);
<trivial group>
gap> S:=SemidirectProduct(A,H);
Error, usage: Group(<gen>,...), Group(<gens>), Group(<gens>,<id>) at /proc/cygdrive/C/gap-4.10.0-x86_64/lib/grp.gi:4563 called from
Group( GeneratorsOfGroup( P ) ) at /proc/cygdrive/C/gap-4.10.0-x86_64/lib/gprd.gi:1115 called from
SemidirectProduct( G, IdentityMapping( G ), N ) at /proc/cygdrive/C/gap-4.10.0-x86_64/lib/gprd.gi:1077 called from
<function "unknown">( <arguments> )
 called from read-eval loop at *stdin*:38
you can 'quit;' to quit to outer loop, or
you can 'return;' to continue

[hulpke]

@ignatsoroko Yes, but that is an issue in SemidirectProduct which call just with the generator list. I will submit a fix.

[ignatsoroko]

You may also would like to change Group(GeneratorsOfGroup(...)) in files:

gap\lib\gprd.gi (SubdirectProduct)
gap\lip\grp.gi
gap\lib\maxsub.gi
gap\lib\oprtglat.gi

[hulpke]

You may also would like to change Group(GeneratorsOfGroup(...)) in files:

Thanks. will fix.

gap\lib\gprd.gi (SubdirectProduct)
gap\lip\grp.gi
gap\lib\maxsub.gi

Here it can't happen, as the group is nonabelian simple.

gap\lib\oprtglat.gi