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Dear GAP Forum,

Gordon Royle asks:

- is the order in which the groups appear arbitrary or are

there some principles underlying it? I notice that the

abelian groups don't seem to appear as the first few groups

of each order; this is mildly surprising for lists of groups,

but maybe there is a deeper underlying principle of which I

am not aware.

Yes, there are clear principles underlying its chosen ordering.

They are described in two sources.

1. "A millenium project: classifying small groups"

by Besche, Eick and O'Brien is a survey paper

on the group construction problem. In addition

to other relevant material, it outlines

some of the organisational principles used.

The preprint of the accepted paper is available

from my homepage

http://www.math.auckland.ac.nz/~obrien

Follow the link to Papers.

2. Some more information on the technical details of the

SmallGroups library can be found on the official homepage

of the SmallGroups project:

http://www.math.rwth-aachen.de/~Hans-Ulrich.Besche/small.html

- is this order guaranteed to remain unchanged (so that if I

refer in a paper to "the 5044th group of order 512" then this

can definitely be recovered by the future reader)

GAP and other systems provide access to the data of the library,

but the responsibility for the library contents rest with

the developers, who guarantee that its current published

ordering will not be changed.

Best wishes,

Eamonn

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