several OEIS items, Dec 02 2007

[N. J. A. Sloane]

site were taking 11 hours to reach me.  Others took 1 minute.
sentences, etc. 
  In most cases there is no need to
 Best regards
 			 Neil
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Message-ID: <3c3af2330712030555uc6e9640o23164d2598cbd2b6 at mail.gmail.com>
Date: Mon, 3 Dec 2007 09:55:24 -0400
From: "Maximilian Hasler" <maximilian.hasler at gmail.com>
To: "Max Alekseyev" <maxale at gmail.com>
Subject: Re: To extend A018216 Maximal number of subgroups in a group with n elements
Cc: "Christian G. Bower" <bowerc at usa.net>, seqfan <seqfan at ext.jussieu.fr>,
   "N. J. A. Sloane" <njas at research.att.com>
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You could add the reference:

    On the Subgroups of an Abelian Group
        G. A. Miller
        The Annals of Mathematics, 2nd Ser., Vol. 6, No. 1. (Oct.,
1904), pp. 1-6.

        Stable URL:
http://links.jstor.org/sici?sici=0003-486X%28190410%292%3A6%3A1%3C1%3AOTSOAA%3E2.0.CO%3B2-P

Paragraph 4 is entitled "total number of subgroups in a group of order p^m"

Maximilian


On Dec 1, 2007 9:27 PM, Max Alekseyev <maxale at gmail.com> wrote:
> On Nov 30, 2007 4:41 PM, Christian G. Bower <bowerc at usa.net> wrote:
> > I think C2^4 has 67 subgroups (1 trivial, 15 C2, 35 C2^2, 15 C2^3, 1 itself).
> > I would suspect that's the largest case, but I'm not in the mood to check all
> > 14 groups of order 16 (and to dig up a description of the more obsure ones.)
>
> I've checked all abelian groups of order 16 and A006116(4)=67 is
> indeed the largest case:
>
> C16 has 5 subgroups
> C2 x C8 has 11 subgroups
> (C2)^2 x C4 has 27 subgroups
> (C2)^4 has 67 subgroups
> (C4)^2 has 15 subgroups
>
> This gives boost to A061034:
>
> %S A061034 1,2,2,5,2,  4,2,16,6,4,  2,10,2,4,4, 67,2,12,2,10, 4,4,2,32,8, 4,28,10,2,8,  2
>
> Neil, please update A061034 accordingly.
>
> Regards,
> Max
>