Dear authors of GAP,

I would like to notify to You the following error, presumably in
PermGroupOps.SemidirectProduct. The error occurs whenever I try
to construct a semidirect product in which the "top" group (i.e.
the nonnormal one) is a permutation group. In the included examples,
I construct a symmetric group of degree 3 by letting a cyclic
(permutation) group of order 2 operate on a cyclic group of order 3
(which is a permutation group in the first example and an AgGroup in
the second one). On the other hand, if I define the cyclic group of
order 2 as an AgGroup (i.e. by

C2 := CyclicGroup(AgWords,2);

then everything seems to work as it should. While I am working with
GAP 3.2.2 (I am using the GAP port of Henry Lakser for the Mac),
I have tested the below examples on the DOS i386 port available on the
Aachen file server, running GAP versions 3.3.0 and the recently released
version 3.4.1. All these show exactly the same behaviour.

In the following examples, my comments are marked ### while the GAP output
is marked #.

################## example 1 #############################
###
### define Sym(3) as a semidirect product ...
###
C3 := CyclicGroup (3);
alpha := GroupHomomorphismByImages (C3,C3,[(1,2,3)],[(1,3,2)]);
A := Group (alpha);
C2 := Group ((10,11));
a := GroupHomomorphismByImages (C2,A,[(10,11)],[alpha]);
G := SemidirectProduct (C2,a,C3);

### then try the following ...

Z := Centre (G);

# Error, Record: element 'MakeMapping' must have an assigned value at
# hom1.operations.MakeMapping( hom2 ) ... in
# map1.operations.CompositionMapping( map2, map1 ) called from
# <rec1> * <rec2> called from
# <rec1> ^ <rec2> called from
# <rec1> ^ <rec2> called from
# arg[1].operations.Stabilizer( arg[1], arg[2], OnPoints ) called from
# ...

FittingSubgroup (G);

# Error, Record: element 'isNilpotent' must have an assigned value at
# if not IsBound( G.isNilpotent ) and G.isNilpotent ... in
# FittingSubgroup( G ) called from
# main loop

Order (G,G.generators[1]);

# Error, Record: element 'Order' must have an assigned value at
# return G.operations.Order( G, g ) ... in
# Order( G, G.generators[1] ) called from
# main loop

##################### example 2 ###########################
LogTo("AgSdir.log");
C3 := CyclicGroup (AgWords,3);
alpha := GroupHomomorphismByImages (C3,C3,[C3.1],[C3.1^2]);
A := Group (alpha);
C2 := CyclicGroup (2);
a := GroupHomomorphismByImages (C2,A,C2.generators,[alpha]);
G := SemidirectProduct (C2,a,C3);
F := FittingSubgroup (G);

# Error, sorry, the elements of <arg> lie in no common ring domain in
# Domain( [ g, h ] ) called from
# SemidirectProductElement( g, g ^ D.mapping, h ) called from
# D.operations.Random( D ) called from
# Random( G ) called from
# G.operations.SylowSubgroup( G, p ) called from
# ...
# brk>

##################### end of example 2 ####################

I hope that the above examples will serve You to locate this error.

Besides, let me include the following question (I know I am not the
first one who asks it, as I found out from the GAP forum messages
distributed with GAP 3.4.1). What about the binary files corresponding
to the MAC ports of GAP that are so frequently announced but never
seem to appear on the file server in Aachen? Is there any other file
server where I might get it? I also noticed that the GAP 3.2.2 port by
Henry Lakser disappeared from ftp.cc.umanitoba.ca. Is he perhaps
releasing a new version? --- If these questions have been answered
recently, as I suppose, could you just send it to me as I have subscribed
gap-forum only a few minutes ago?

Best regards,

Burkhard H”fling, Uni Mainz.