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Dear GAP Forum,

The recently released bugfixes fixed a number of *dangerous* bugs in GAP, that

is bugs that could cause a computation to produce a wrong result without

warning. Although we think it unlikely, this could result in users having

arrived at plausible but incorrect mathematical results. To help you decide if

you might be in this position, this mail gives more details of the exact

effect of the bugs, and the dates on which they were introduced into GAP.

One of these bugs dates from GAP 3.1, and we said in the announcement of

bugfix4 that no fix was available for this bug in GAP3. In fact we now have a

fix, and will release it as soon as possible. Since this is the first change

to the GAP3 kernel for more than two years, you will appreciate that getting

all the necessary versions compiled, and preparing the fix is not a routine

task.

In a subsequent announcement, we will say more about our policy for

maintenance of GAP3, but in the meantime, we would urge all users who can to

move to GAP4.

Finite field exponentiation bugs ================================ The first finite field bug:

The bug affected the computation of powers of elements in a finite

field in the following situation and could produce wrong results.(Z(q)^m)^n where m>0, n>0 and m*n > 2^31-1 and (Z(q)^m)^-n where m>0, n>0 and (q-m)*n > 2^31-1This bug has been there since the first release of GAP 4 and in

fact goes back to the first release of GAP 3. It is fixed by bugfix #4.

The second finite field bug:

Fixing the previous bug introduced another one which also affected

the computation of powers of elements in a finite field in the

following situation:

(0*Z(q))^m was evaluated incorrectly to one when m was a

multiple of q-1.This bug has been there since bug fix #4.

Polycyclic Groups Bug =====================

This bug affects PrimePowerComponents for PcGroups (and consequentially

`SpecialPcgs' and everything that builds on top of it) for groups with at

least three distinct primes dividing their order. It was introduced to the

development version in May 1999 and so was released for the first time in GAP

4.1. In particular, the beta versions of GAP 4 did not contain this bug.

Primitive Groups Database Bug =============================

Among the things fixed in bugfix 4, which were not explicitly mentioned is a

small bugfix to the library of primitive groups.

The error (which was reported by Christial Pech -- many thanks again!)

affected the primitive groups of degree 325 and 756, among these groups were

some which were of the right *isomorphism type* but in the wrong

*permutation representation*, that is they were of the wrong permutation

degree.

This error was due to a misinterpretation of information from the printed

version of the classification of primitive groups in [Dixon, Mortimer].

The error is fixed and tests have been run to ensure that all groups in this

library now are of the right degree.

Steve Linton

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