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Erhard Aichinger asked:

I am using

TwoGroup (32, 6)

to get the 6th group of order 32. Do you

know whether the numbering of groups in the twogroup-package is

identical to the numbering in the book

Thomas, A.D., and Wood G.V., Group Tables, Shiva Publishing Ltd. ?

The answer is : no, the numbering schemes are non-identical.

According to their preface, Thomas and Wood follow the numbering in

Hall/Senior (The groups of order 2^n, n<=6), except for abelian

groups.

The numbering in the two-groups library of GAP is the one by Newman

and O'Brien which is determined by their specific p-group generation

algorithm. (see remark and references in the description of the

two-group library in the chapter 'Group Libraries' of the GAP manual).

You can get some information about different namings by using the

function 'GroupId', described in the chapter 'Groups' in the manual.

So for the group obtained in GAP by TwoGroup (32, 6) the function

GroupId gives (i.a.) 'catalogue := [32, 46]' and the group has indeed

number 46 both in Hall/Senior and in Thomas/Wood.

Note however that for abelian groups there are still little

differences in the numbering by Hall/Senior and the number given by

the entry 'catalogue'. Therefore for abelian groups you should best

use the function 'AbelianInvariants', also described in the chapter

'Groups' in the manual, to see what you have got. This function

should, however, ONLY BE APPLIED TO ABELIAN GROUPS, as said in the

manual. If you are not sure if your group is abelian you can first use

the function 'IsAbelian' to test this.

WARNING: At present the function 'AbelianInvariants' applied to a

nonabelian group will sometimes (e.g. for finitely presented groups)

determine the abelian invariants of its commutator factor group, but

sometimes it may produce some rather ununderstandable error message

and, worst of all, for nonabelian ag groups it may produce a

syntactically innocent looking wrong result. We intend to change the

function so that it will always produce the abelian invariants of the

commutator factor group, but this will only be in a forthcoming

release.

Sorry for the inconvenience, but agreeing about a naming scheme, such

as in Chemistry, is too difficult for mathematicians.

Joachim Neubueser

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