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

1,6

Comments

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

Links

Eric M. Schmidt, Table of n, a(n) for n = 1..2000

MathOverflow, Center of p-groups

Formula

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

Example

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

Prog

(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

Crossrefs

Cf. A059806, A051532.

Sequence in context: A016470 A369068 A347395 * A214208 A279965 A285121

Adjacent sequences: A059804 A059805 A059806 * A059808 A059809 A059810

Keyword

nonn

Author

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

Extensions

More terms from Eric M. Schmidt, Sep 20 2012

Status

approved