A059807 Maximal size of the commutator subgroup of G where G is a finite group of order n.

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

Offset: 1

Author

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

Keywords

• nonn

Comments

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

Examples

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

Links

• Eric M. Schmidt, Table of n, a(n) for n = 1..2000
• MathOverflow, Center of p-groups

Crossrefs

Cf. A059806, A051532.

Programs

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

Formula

For prime p and m >= 2, a(p^m) = p^(m - 2). - Eric M. Schmidt, Sep 20 2012

Extensions

More terms from Eric M. Schmidt, Sep 20 2012