Dear GAP Forum members,
I have the pleasure to announce the release of two new GAP4 share
by Burkhard Hoefling
by Bettina Eick and Charles Wright.
Both provide tools for the investigation of the subgroup structure of
finite soluble groups.
The starting point of the development of a special theory about the
subgroup structure of finite soluble groups was the discovery by
Philip Hall in 1928 of what are now called Hall subgroups and in
particular Sylow complements (and, in 1937, that in fact solubility is
characterised by the existence of Sylow p-complements for all primes p
dividing the order of the group). System normalizers (also 1937) and
Carter subgroups (1961) were the next characteristic classes of
conjugate subgroups in soluble groups discovered until in the sixties
Gaschuetz, Fischer, Hartley, and Schunck described very general
methods to define characteristic conjugacy classes of subgroups in
finite soluble groups of which the previously mentioned are special
A comprehensive description of the present state of the theory of
finite soluble groups is given in
K. Doerk and T.O. Hawkes,
Finite soluble groups.
W. de Gruyter, 1992.
The two share packages announced above provide access to the explicit
construction of such characteristic classes of subgroups and beyond
open up new ways of e.g. finding normal subgroups or complements of
elementary abelian normal subgroups in finite soluble groups.
CRISP also deals with more general group classes, while FORMAT follows
more closely the theory of formations that was initialized by
Gaschuetz. So there is a certain overlap in the functionality of the
two packages, which were developed independently. Since they employ
different methods in most of these overlap cases this provides a
welcome opportunity for cross checking and comparison of methods.
Via the GAP web pages there is access to Readme files, the manuals as
well as to two papers describing the respective mathematical
background and newly developed algorithms.
The FORMAT package is the successor of a GAP3 package on Formations
that some of you may know already.
As editor of the two packages it is my pleasure to thank not only the
authors for a very nice extension of the capabilities of GAP, that
should be helpful both for research on soluble groups and teaching
group theory, but also the two referees (who stay anonymous as usual
with referees of published papers) who have done a most careful job of
testing the packages and have provided very helpful suggestions for
PS. Please note that at present, due to some technical problem, the
packages are not yet available on the Australian server. Please use
one of the other servers.