> < ^ Date: Tue, 08 Jun 1999 14:02:08 +0300
> < ^ From: Alexander B. Konovalov <alexk@mcs.st-and.ac.uk >
> ^ Subject: [2] Unit groups in Sisyphos

Dear GAP-forum,
Sorry, it seems now that my last request to forum wasn't absolutely correct,
but this lead to several useful hints. As you possibly remember, I've asked:

does anybody know what hardware resources are necessary to compute
normalized units group of group algebra of group of order 32 over GF(2),
using the function NormalizedUnitsGroupRing ?

So, I have discovered, that really I have no problems with calculation of
NormalizedUnitsGroupRing(G) even if Size(G)=128.
The actual problem is as follows:

gap> G:=TwoGroup(32,10)
Group( a1, a2, a3, a4, a5 )
gap> U:=NormalizedUnitsGroupRing(G);
#D use multiplication table
Group( g1, g2, g3, g4, g5, g6, g7, g8, g9, g10, g11, g12, g13,
g14, g15, g16, g17, g18, g19, g20, g21, g22, g23, g24, g25,
g26, g27, g28, g29, g30, g31 )
gap> C:=Centre(U);
Subgroup( Group( g1, g2, g3, g4, g5, g6, g7, g8, g9, g10, g11,
g12, g13, g14, g15, g16, g17, g18, g19, g20, g21, g22, g23,
g24, g25, g26, g27, g28, g29, g30, g31 ), [ g3,
g4*g7*g9*g13*g14*g16*g22, g10, g11*g15*g17*g21, g18, g19,
g23, g25, g26, g28, g29, g30, g31 ] )
gap> D:=Difference(U,C);
gap: sorry, cannot extend the workspace, maybe use option '-a <memory>'?

As I could understand, this function calls to Elements(G), and (thanks to
Dr. Andrew C. Aitchison), now I could realize how expensive is this,
so it will be better to try to improve algorithm of my problems solving.

The next question is very similar to the previous one :-)
does anybody know what hardware resources are necessary to compute
normalized units group of group algebra of group of order ***256*** over
GF(2), using the function NormalizedUnitsGroupRing ?
Here I have the following situation:

gap> G:=TwoGroup(256,10);
Group( a1, a2, a3, a4, a5, a6, a7, a8 )
gap> RequirePackage("sisyphos");
gap> U:=NormalizedUnitsGroupRing(G);
#D use multiplication table
fatal error: memory exhausted
Error, output file was not readable in
NormalizedUnitsGroupRing( G ) called from
main loop
brk>

The reason for such calculation is connected with
the problem of involving of certain wreath products
into the unit group of modular group algebras

Sincerely yours,
Alexander B. Konovalov,
Algebra and Geometry Chair,
Zaporozhye State University, Zaporozhye, Ukraine.
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Fax: (38-0612) 32 59 36
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E-mail: konovalov@member.ams.org

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