OFFSET
1,36
COMMENTS
A group of order n is Lagrangian if it has a subgroup of order d for each divisor d of n.
LINKS
Mathematics StackExchange Discussion, Complete classification of the groups for which converse of Lagrange's Theorem holds
PROG
(GAP)
a:=function(n)
local i, N, G, m;
N:=NumberSmallGroups(n);
m:=0;
for i in [1..N] do
G:=SmallGroup(n, i);
if Set(List(ConjugacyClassesSubgroups( G ), t->Size(Representative(t)))<>DivisorsInt(n)
then m:=m+1; fi;
od;
return m;
end;;
CROSSREFS
KEYWORD
nonn
AUTHOR
W. Edwin Clark, Feb 20 2017
STATUS
approved