Dear Mrs. and Mr. Forum,
Andries Brouwer asks two questions concerning vector spaces, namely
whether elementary abelian groups can be regarded as vector spaces
and vice versa, and whether it is possible to describe the action of
a group on an elementary abelian subgroup via a matrix representation.
Here 'regard' and 'describe' apparently both mean that one has homomorphisms
between the group and the vector space resp. between the group and the
representation and its module. As stated recently in another message
to the GAP forum, up to now there is no developed data structure
representing vector spaces and modules in GAP, so the desired homomorphisms
would not be of much help. But as soon as these domains and some functions
dealing with them are available in GAP (hopefully in the next version),
the questions of Andries Brouwer can be answered 'yes'.
P.S.: What Andries Brouwer tells about the strange behaviour of '~'
of course describes a bug, but I cannot say anything about when
it will be fixed.