problem with the documentation of FamilyPcgs

[ThomasBreuer]

The documentation of FamilyPcgs says:

‣ FamilyPcgs( grp ) ────────────────────────────────────────────── attribute
  
returns  a  "natural"  pcgs  of  a  pc group grp (with respect to which pcgs
operations as described in Chapter 45 are particularly efficient).

This is true only if grp is a "full pc group".
If grp is a subgroup then the family pcgs of the full group is returned.

gap> g:= DihedralGroup(8);
<pc group of size 8 with 3 generators>
gap> c:= Centre(g);
Group([ f3 ])
gap> FamilyPcgs( g );
Pcgs([ f1, f2, f3 ])
gap> FamilyPcgs( g ) = FamilyPcgs( c );
true

Note that IsPcGroup returns true also for subgroups of full pc groups.
(The situation is different for fp groups, there we have IsFpGroup only for the full group, and IsSubgroupFpGroup for subgroups.)

By the way: What is the recommended way to find out whether a given pc group grp is in fact a full pc group?
One can of course check whether grp contains FamilyPcgs( grp ), but is there an easier way?

[hulpke]

It probably should say: of a group A, containing grp, with A chosen maximal.

It might be worth to align language with the documentation for HomePcgs.

[ThomasBreuer]

@hulpke Thanks. I am going to create a pull request for that.

[ThomasBreuer]

Concerning HomePcgs mentioned by @hulpke, this function is undocumented, as well as the concept of home pcgs. The term "home" in the sense of "home pcgs" still occurs in a few places in the Reference Manual:

• The documentation of ClassesSolvableGroup mentions home pcgs.
• The documentation of ExtendedPcgs erroneously refers to home as if it were the name of an argument. A possible fix would be to remove this reference. (Anyhow, the documentation of ExtendedPcgs is not really helpful. Moreover, all calls of ExtendedPcgs in the GAP library except one are commented out, and the one exception is inside the undocumented function TailOfPcgsPermGroup.)

[fingolfin]

@ThomasBreuer Has this been resolved by PR #5488? If not, what is left to be done?

[ThomasBreuer]

The original problem is solved.

@hulpke had suggested to achieve some consistency in the documentation of FamilyPcgs and HomePcgs. The latter is undocumented, so I do not know how to proceed with this suggestion.

[ThomasBreuer]

@hulpke I have not dealt with HomePcgs in #5488, but you had mentioned HomePcgs in a comment. Shall we change something about it, or close this issue?

[hulpke]

@hulpke I have not dealt with HomePcgs in #5488, but you had mentioned HomePcgs in a comment. Shall we change something about it, or close this issue?

I think close -- I just wanted to alert everyone that there is a related issue for HomePcgs.