Timeline for Largest permutation group without 2-cycles or 3-cycles

4 events

when toggle format	what		by	license	comment
Jan 11, 2013 at 5:19	vote	accept	rishig
Jan 11, 2013 at 5:19
Jan 10, 2013 at 9:42	comment	added	Michael Giudici		It is known that the only primitive group on $n$ points containing a 2-cycle is $S_n$ and any primitive group containing a 3-cycle contains $A_n$. These are classical regults going back to Jordan. Thus any primitive group other than $A_n$ or $S_n$ has no 2-cycles or 3-cycles. There are very good upper bounds on the order of primitive group. The best is by Maroti which says that for such primitive groups one of the following holds: - G is a Mathieu group $M_n$ for $n=11,12,23,24$ -G is a subgroup of $S_m wr S_k$ with $n=m^k$, $m\geq 5$ and $k\geq 2$ -\|G\|\leq n^{1+\lfloor log_2(n)\rfloor}$
Jan 10, 2013 at 3:31	history	edited	Dima Pasechnik	CC BY-SA 3.0	bigger group!
Jan 10, 2013 at 3:21	history	answered	Dima Pasechnik	CC BY-SA 3.0