Dear GAP-Forum.

In his letter, Michael Cherkassoff wrote:

I have some problems with (I guess) implementation of GAP.

I do work with finite Projective Special Linear Groups. At the
moment they are being represented as some permutation groups

[...]

For these cases GAP can construct the group,
calculate the size,
construct conjugacy classes,

but it can't calculate centralizer of the element.

If you get the conjugacy classes, each class has an entry .centralizer,
which contains the centralizer of the class representative.

I did the job in background with redirecting of input-output and
GAP would just stop working without any error message.

In this case, the job grew too large for the system, and thus died.

So is it a bug in GAP (I can provide exact text of the program to nail it) or
is it just natural restriction of the size?

The restriction is by the size, the operating system allows for GAP.

Also I would appreciate very much the help on how to collect all
involutions in the group. Now I'm doing by computation of all
conjgacy classes (which I don't need) and then picking ones with
elements of order 2.

I don't think, this is the way one should do it. First, all these groups
have relatively few classes of involutions. The character table
will show you how many classes of involutions exist. Then searching for
random elements of even order and powering them should yield you
representatives for the classes easily. (By creating the corresponding
ConjugacyClass es, one can check for conjugacy using the 'in' command.)

However, it should be also possible to obtain these representatives by
using the normal form of matrices, as L(n,q) does not differ too much from
GL(n,q).

Alexander Hulpke