

A208235


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


1



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

1,2


LINKS

Table of n, a(n) for n=1..13.
MathOverflow, Largest permutation group without 2cycles or 3cycles


EXAMPLE

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



