[seqfan] Re: Symmetric groups
W. Edwin Clark
wclark at mail.usf.edu
Mon Nov 28 01:20:07 CET 2016
No, S_5 does not have a subgroup of order 15 says GAP. Here's GAP code
which gives the orders
of the subgroups of S_5:
G:=SymmetricGroup(5);;
C:=ConjugacyClassesSubgroups(G);;
OrdersSubgroupsS_5:=Set(ListX(C,t->Size(Representative(t))));
[ 1, 2, 3, 4, 5, 6, 8, 10, 12, 20, 24, 60, 120 ]
On Sun, Nov 27, 2016 at 4:14 PM, Frank Adams-Watters <franktaw at netscape.net>
wrote:
> If n divides m!, does the symmetric group S_m always have a subgroup of
> order n?
>
> If so, a comment should be added to A002034 that a(n) is the genus of the
> smallest symmetric group with a subgroup of order n. If not, where is the
> first exception? (8 in S_4?) Is the sequence so described in the OEIS? If
> not, it should be added.
>
> Franklin T. Adams-Watters
>
>
> --
> Seqfan Mailing list - http://list.seqfan.eu/
>
More information about the SeqFan
mailing list