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A059807
Maximal size of the commutator subgroup of G where G is a finite group of order n.
3
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
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
Sequence in context: A369068 A375961 A347395 * A214208 A279965 A285121
KEYWORD
nonn
AUTHOR
Noam Katz (noamkj(AT)hotmail.com), Feb 24 2001
EXTENSIONS
More terms from Eric M. Schmidt, Sep 20 2012
STATUS
approved