[r-t] Group Theory again

[Robin Woolley]

Hi all,

Firstly, belated thanks to Martin, David & Richard for their comments on 31st January. Such is the way of things, of course, that within 10 minutes of sending my request I found Lagrange's Thm. in an old text-book.

Today's request for help: I get the impression that, given two subgroups, it is  a non-trivial problem to find the smallest subgroup containing both. Is this correct? Example, consider S4 and subgroups generated by <1423> and <2413> of order 3 and 4 respec. It is not obvious, but it seems that the smallest group containing these elements is S4 itself. 

Best wishes
Robin

b.t.w., thanks especially for the link to Landau's Formula. It prompted me to devise the following 12 part:

6720 P B Major
        1 4 7
4235678     -
5324867 s 1 s
2534867     -
3254867     -
3524867     s
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://bellringers.net/pipermail/ringing-theory_bellringers.net/attachments/20130214/274038ce/attachment.html>