[GAP Forum] reza orfi

Bettina Eick beick at tu-bs.de
Thu Oct 28 09:38:58 BST 2004

Dear GAP Forum, dear Reza Orfi,

you wrote:
> I need all groups of order 3^7,3^8,3^9,3^10,5^7,5^8,5^9,5^10.
> but there are not in gap4r4. please help me .i need this group .

it is true that the groups of your considered orders are not available
in GAP. For many of these orders an explicit determination of these
groups has not been done yet and would probably be difficult.

For example, consider the groups of order p^10. For p=2, these groups
have been enumerated and thus it is known that there are 49487365422
groups of order 2^10. (See: B. Eick, E. O'Brien. Enumerating p-groups.
J. Austral. Math. Soc. 67, 191 - 205 (1999).) As this is a very large
number, we did not attempt to list the groups of order 2^10 explicitly
or to include them in an electronic database.

This problem is going to be worse for the groups of order 3^10 and 5^10.
The groups of these orders have not been enumerated or listed yet and it
seems unlikely that this will happen soon.

For the smallest of your orders, (e.g. 3^7,) it may be possible to list
all or at least the interesting groups explicitly, if you are willing
to invest time and effort in it. In principle, the p-groups of order p^n
can be determined (up to isomorphism) using the p-group generation
algorithm by E. O'Brien. This is available in the ANUPQ package of GAP.

A good strategy in your case might be to try to restrict the groups that
you need first and then try to list these groups with p-group generation.
If you find a suitable restriction, then this approach might work.

Hope this helps,

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