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Dear GAP Forum members,

I have the pleasure to announce the release of two new GAP4 share

packages:

CRISP

by Burkhard Hoefling

and

FORMAT

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

cases.

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

local improvements.

Joachim Neubueser

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.

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