OFFSET
1,1
COMMENTS
Pálfy proved there are no primitive solvable permutation groups T with order greater than n^c_3 / 24^(1/3) but infinitely many for which equality is attained, where n is the degree of the group. Such groups necessarily have degree which is a power of 3, hence the subscript. He also gave tighter bounds for other prime powers.
LINKS
P. P. Pálfy, A polynomial bound for the orders of primitive solvable groups, J. Algebra 77:1 (1982), pp. 127-137.
EXAMPLE
E(9) : 2S_4 is a primitive solvable permutation group of degree 9 and order 432 = 9^(5/3 + log_9(32))/24^(1/3).
MATHEMATICA
RealDigits[5/3+Log[9, 32], 10, 120][[1]] (* Harvey P. Dale, Mar 05 2015 *)
PROG
(PARI) 5/3+log(32)/log(9)
CROSSREFS
KEYWORD
AUTHOR
Charles R Greathouse IV, Jun 04 2014
STATUS
approved