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 A208235 Maximal order of a subgroup of the symmetric group of degree n that contains no 3-cycle. 1
 1, 2, 2, 8, 20, 120, 168, 1344, 1512, 3840, 7920, 95040, 95040 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS 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

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Last modified January 20 13:10 EST 2019. Contains 319330 sequences. (Running on oeis4.)