A208235 Maximal order of a subgroup of the symmetric group of degree n that contains no 3-cycle.

1, 2, 2, 8, 20, 120, 168, 1344, 1512, 3840, 7920, 95040, 95040

Offset

1,2

Links

Table of n, a(n) for n=1..13.

MathOverflow, Largest permutation group without 2-cycles or 3-cycles

Example

A Sylow 2-subgroup of S_4 is of order 8, and contains no 3-cycle. The only subgroups of S_4 with more than 8 elements are A_4 and S_4, which both contain 3-cycles. So a(4) = 8.

Prog

(GAP)
Has3:=function(G, n)
local x, p;
for p in Elements(G) do
  x:=Product(CycleLengths(p, [1..n]));
  if  x = 3 then return true; fi;
od;
return false;
end;;
a:=function(n)
local MM, h, nn;
MM:=0;;
for H in ConjugacyClassesSubgroups(SymmetricGroup(n)) do
  h:=Representative(H);
  if Size(h)<=MM then continue; fi;
  if Has3(h, n) = false then
    nn:=Size(h);
    if nn > MM then MM:=nn; Mg:=h; fi;
  fi;
od;;
return MM;
end;;

Crossrefs

Cf. A208232.

Sequence in context: A259807 A137774 A167532 * A151377 A151407 A130102

Adjacent sequences: A208232 A208233 A208234 * A208236 A208237 A208238

Keyword

nonn,more

Author

W. Edwin Clark, Jan 10 2013

Extensions

a(10)-a(13) from Stephen A. Silver, Feb 14 2013

Status

approved