cp's OEIS Frontend

A059806 Minimal size of the center of G where G is a finite group of order n.

%I A059806 #14 Sep 16 2012 22:44:27
%S A059806 1,2,3,4,5,1,7,2,9,1,11,1,13,1,15,2,17,1,19,1,1,1,23,1,25,1,3,2,29,1,
%T A059806 31,2,33,1,35,1,37,1,1,2,41,1,43,2,45,1,47,1,49,1,51,1,53,1,1,1,1,1,
%U A059806 59,1,61,1,3,2,65,1,67,1,69,1,71,1,73,1,1,2,77,1
%N A059806 Minimal size of the center of G where G is a finite group of order n.
%C A059806 a(n) = n if and only if n belongs to sequence A051532 - Avi Peretz (njk(AT)netvision.net.il), Feb 27 2001
%C A059806 a(n) = 1 if and only if n occurs in A060702. - _Eric M. Schmidt_, Aug 27 2012
%H A059806 Eric M. Schmidt, <a href="/A059806/b059806.txt">Table of n, a(n) for n = 1..2000</a>
%H A059806 MathOverflow, <a href="http://mathoverflow.net/questions/107182/center-of-p-groups">Center of p-groups</a>
%F A059806 For prime p and m >= 3, a(p^m) = p. - _Eric M. Schmidt_, Aug 27 2012
%e A059806 a(6) = 1 because the symmetric group S_3 has trivial center.
%o A059806 (GAP) A059806 := function(n) local min, fact, i; if (n mod 6 = 0) then return 1; fi; if (IsPrimePowerInt(n)) then fact := Factors(n); if (Length(fact) <> 2) then return fact[1]; fi; fi; min := n; for i in [1..NumberSmallGroups(n)] do min := Minimum(min, Size(Center(SmallGroup(n, i)))); if (min = 1) then break; fi; od; return min; end; # _Eric M. Schmidt_, Aug 27 2012
%Y A059806 Cf. A059807, A051532.
%K A059806 nonn
%O A059806 1,2
%A A059806 Noam Katz (noamkj(AT)hotmail.com), Feb 24 2001
%E A059806 More terms from _Eric M. Schmidt_, Aug 27 2012