Re: subgroups of S_n
- From: Jack Schmidt <Jack.Schmidt.SciMath@xxxxxxxxx>
- Date: Thu, 27 Mar 2008 21:09:49 EDT
(1) Consider the subgroup H_i = {s in S_n : s(i) = i}
for some 1 =< i =< n.
Why does H have order (n-1)! Is it isomorphic to
S_{n-1} ?
Orbit-Stabilizer, yes.
(2) Does every subgroup of index n in S_n arise in
this way?
That is, is every subgroup of index n in S_n equal to
H_i for some i ?
Not for n=6, but for other n yes.
.
- Prev by Date: Rudin problem
- Next by Date: Blood eating is banned in islam
- Previous by thread: Rudin problem
- Next by thread: Blood eating is banned in islam
- Index(es):
