(Again) Number of rotation subgroups of S_n

[simone at cs.york.ac.uk]

Dear seqfans,

On the 10/10/2005 Neil Sloane posted the following message:

>A friend suggested the following set of sequences

>Let S_n be the symmetric group of all perms of n letters,
>of order n!

>A transposition is a permutation like (3,5).
>A reflection is any element of order 2, that is, a product of disjoint
>transpositions
>A "rotation" is a product of two transpositions, not necessarily
disjoint, >so either (1,2,3) or (1,2)(3,4), etc.

>Questions:
>How many subgroups of S_n have the property that they are
>generated by rotations?
>How many non-isomorphic ones?

>How many subgroups of S_n have the property that they are
>generated by reflections?  (Is this the Bell numbers, A000110 ?)
>How many non-isomorphic ones?  (Again, this may be a well-known sequence)

>Same two questions for groups generated by rotations AND reflections?

>NJAS

Now, Peter Cameron has written the attached working notes. However, the
problem is not solved yet, and I am working on it.

Is there anybody who has time to help me?

Thanks and best regards,
Simone

--
Simone Severini
Department of Mathematics and Department of Computer Science
University of York, YO10 5DD York, U.K.
Tel: +44 (0)1904 433072
Web: www-users.york.ac.uk/~ss54
-------------- next part --------------
A non-text attachment was scrubbed...
Name: application2f.pdf
Type: application/pdf
Size: 24185 bytes
Desc: not available
URL: <http://list.seqfan.eu/pipermail/seqfan/attachments/20051115/478028b9/attachment.pdf>