A104114 The order of the smallest solvable group with derived length n.

1, 2, 6, 24, 48, 432, 1296

Offset

0,2

Comments

At order 24, the two groups which achieve the maximum derived length are S_4 and SL(2,3). At order 48, a group which achieves the maximum derived length is GL(2,3). At order 432, the only group which achieves the maximum derived length is 3^2:GL(2,3).

There are three groups of order 1296 achieving maximal derived length. - Charles R Greathouse IV, May 26 2014

Links

Table of n, a(n) for n=0..6.

Formula

a(n) >= 2*a(n-1). - Charles R Greathouse IV, May 26 2014

Example

a_2=6 because the smallest solvable group with derived length 2 is the symmetric group S_3, which has order 6.

Prog

(GAP) a := function(arg)
    local n, size, gr;
    n := arg[1];
    if Length(arg) > 1 then
        size := arg[2];
    else
        size := 1;
    fi;
    gr := OneSmallGroup(Size, size, DerivedLength, n);
    if gr <> fail then
        return size;
    else
        return a(n, size + 1);
    fi;
end;  # Charles R Greathouse IV, May 23 2014

Crossrefs

Sequence in context: A189851 A189563 A321613 * A175624 A289161 A118038

Adjacent sequences: A104111 A104112 A104113 * A104115 A104116 A104117

Keyword

nice,nonn,hard,more

Author

David L. Harden, Mar 31 2005

Extensions

a(6) from Charles R Greathouse IV, May 26 2014

Status

approved