[GAP Forum] New version of the LAGUNA package for group rings

[Alexander Konovalov]

Dear GAP Forum,

Let  me  announce the next version 3.3 of the LAGUNA package for GAP4,
developed  by  Victor  Bovdi,  Richard Rossmanith, Csaba Schneider and
myself.

LAGUNA  extends  GAP4  functionality  for computations in group rings.
Besides  computing  some  general  properties  and attributes of group
rings  and their elements, LAGUNA is able to perform two main kinds of
computations.  Namely,  it  can  verify  whether  a group algebra of a
finite  group  satisfies  certain Lie properties, and it can calculate
the  structure  of  the  normalized unit group of a group algebra of a
finite p-group over the field of p elements.

List of new features and fixed bugs in the version 3.3:

*  Functions  for fast construction of left/right/two-sided group ring
ideals  generated  by elements of the form h-1, where h in H\{1} and H
is  a  subgroup of the underlying group (contributed by my PhD student
Anastasiya Tsapok).

*   Method   for   getting   random   elements   from   Units(KG)  and
NormalizedUnitGroup(KG),  taking  them randomly from KG until we get a
unit; in the normalized case augmentation is adjusted to one.

*  Method  for the embedding of the subgroup of an underlying group to
the normalized unit group given by the power-commutator presentation.

*   Operation  'PartialAugmentations'  returning  a  list  of  partial
augmentations  of  an  element  of  a  group  ring  and  corresponding
conjugacy classes (contributed by my PhD student Anastasiya Tsapok).

* New attribute 'LieDerivedLength' for Lie algebras

* Computation of bicyclic units and of the bicyclic unit group.

*  Computation  of  the  unitary subgroup of the normalized unit group
(immediate method for small groups).

* computation of the Lie upper codimension series of finite p-groups.

* Fixed bugs:

-    Replaced   'GeneratorsOfGroup'   to   'MinimalGeneratingSet'   in
DimensionBasis to fix a bug with SmallGroup(512,2).

-  Adjusted LieDerivedSubalgebra for the compatibility with the Sophus
package by Csaba Schneider.

- Fixed a bug with the nilpotency index of the augmentation ideal when
p>2 (thanks to Inger Christin Borge for reporting this bug!).

-  Fixed a bug with 'IsUnit' and 'InverseOp' for elements of order q^n
in characteristic p when (p,q)=1.

-  Added  SetIsPGroup(U,true)  for  normalized  unit groups of modular
group  algebras  of  finite p-groups for correct method selection (for
example, for the computation of their automorphism groups with AutPGrp
package).

The  new  version of the package is available from the LAGUNA homepage
at  http://ukrgap.exponenta.ru/laguna.htm  and  from  the GAP homepage
http://www.gap-system.org/.


Sincerely yours,
Alexander Konovalov