A059807 - OEIS

%I #7 Sep 20 2012 17:03:12

%S 1,1,1,1,1,3,1,2,1,5,1,4,1,7,1,4,1,9,1,5,7,11,1,12,1,13,3,7,1,15,1,8,

%T 1,17,1,9,1,19,13,10,1,21,1,11,1,23,1,24,1,25,1,13,1,27,11,14,19,29,1,

%U 60,1,31,7,16,1,33,1,17,1,35,1,36,1,37,25,19,1

%N Maximal size of the commutator subgroup of G where G is a finite group of order n.

%C a(n) = 1 iff n belongs to sequence A051532. - Avi Peretz (njk(AT)netvision.net.il), Feb 27 2001

%H Eric M. Schmidt, <a href="/A059807/b059807.txt">Table of n, a(n) for n = 1..2000</a>

%H MathOverflow, <a href="http://mathoverflow.net/questions/107182/center-of-p-groups">Center of p-groups</a>

%F For prime p and m >= 2, a(p^m) = p^(m - 2). - _Eric M. Schmidt_, Sep 20 2012

%e a(6) = 3 because the commutator subgroup of the symmetric group S_3 is the group Z_3.

%o (GAP) A059807 := function(n) local max, fact, i; if (IsPrimePowerInt(n)) then fact := Factors(n); if (Length(fact) >= 2) then return n/fact[1]^2; fi; fi; max := 1; for i in [1..NumberSmallGroups(n)] do max := Maximum(max, Size(DerivedSubgroup(SmallGroup(n, i)))); od; return max; end; # _Eric M. Schmidt_, Sep 20 2012

%Y Cf. A059806, A051532.

%K nonn

%O 1,6

%A Noam Katz (noamkj(AT)hotmail.com), Feb 24 2001

%E More terms from _Eric M. Schmidt_, Sep 20 2012