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Dear Members of the GAP Forum,

It is a pleasure to announce the new GAP4 share package

`AClib'

by Bettina Eick and Karel Dekimpe.

`AClib' stands for `almost crystallographic groups library'.

A group is called almost crystallographic if it is finitely

generated nilpotent-by-finite and has no non-trivial finite

normal subgroups. Further, an almost crystallographic group

is called almost Bieberbach if it is torsion-free.

The almost crystallographic groups of Hirsch length 3 and a

part of the almost cyrstallographic groups of Hirsch length 4

have been classified by Dekimpe in [1]. This classification

includes all almost Bieberbach groups of Hirsch lengths 3 or 4.

The AClib package gives access to this classification; that is,

the package contains the library of groups as classified in [1]

in a computationally useful form.

The groups in this library are available in two different

representations. First, each of the groups of Hirsch length

3 or 4 has a rational matrix representation of dimension 4

or 5, respectively. These matrix representations have been

determined in [1] and they are included in `AClib'. Secondly,

all the groups in this libraray are (infinite) polycyclic groups

and the package also incorporates polycyclic presentations for

them. These presentations can be used to compute with the given

groups using the methods of the `Polycyclic' package of GAP4.

[1] K. Dekimpe. Almost-Bieberbach Groups: Affine and Polynomial

Structures. Springer Lecture Notes in Mathematics, Volume 1639

(1996)

AClib can be obtained from the web page

http://www-gap.dcs.st-and.ac.uk/~gap/Info4/share.html

and from the GAP4 share packages ftp directory:

ftp://ftp-gap.dcs.st-and.ac.uk/pub/gap/gap4/share

Questions concerning the package or its installation should be

addressed to: eick@mathematik.uni-kassel.de

Gerhard Hiss

February 22, 2001

-- Gerhard Hiss Lehrstuhl D fuer Mathematik, RWTH Aachen Templergraben 64, 52062 Aachen Tel.: (+49) (0) 241 / 80-4543

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