documentation of `EpimorphismSchurCover`

[ThomasBreuer]

Currently the documentation of EpimorphismSchurCover says

‣ EpimorphismSchurCover( G[, pl] ) ─────────────────────────────── attribute

returns an epimorphism epi from a group D onto G. The group D is one (of possibly several) Schur covers of G. The group D can be obtained as the Source (32.3-8) value of epi. The kernel of epi is the Schur multiplier of G. If pl is given as a list of primes, only the multiplier part for these primes is realized. At the moment, D is represented as a finitely presented group.

The last sentence is not correct, one can get an epimorphism from a matrix group if G is a natural alternating or symmetric group.

What is the right strategy to deal with such situations:
Shall we just remove the wrong statements, or shall we replace them by something that explains what happens in the generic case, and that "better" results can be returned in special cases.
And would it be appropriate to provide EpimorphismSchurCover( IsFpGroup, G ), in order to force an epimorphism from a f.p. group?

[jackschmidt]

Two more cases where D is represented differently is for Pcp groups (where D is also a Pcp group), or trivial groups with pi specified (where D = G)

It seems like the last sentence is mostly a warning for finite solvable groups (where D could have been represented as a PcGroup, but is instead represented as an FpGroup), so I like the "explain what happens in the generic case..." or "just remove the wrong statements".

I don't have a strong opinion on the IsFpGroup version. One can always use IsomorphismFpGroup on G to use the SchurCoverFp and Tietze simplifications code, but if someone is requesting the FpGroup explicitly, it might be nice to write it for them (especially if the following is not the right way to do it).

EpimorphismSchurCoverAsFpGroup := function(grp)
  local iso, epi;
  iso := IsomorphismFpGroup(grp);
  epi := EpimorphismSchurCover(Image(iso));
  return epi*InverseGeneralMapping(iso);
end;