Let $g_1, \ldots, g_k$ be distinct permutations on a set $\Omega$. Suppose that $G = \langle g_1, \ldots, g_k \rangle$ is an abelian permutation group with only elements of order at most 2. Is it possible that $|G| = k$? If not, can $|G|$ be polynomial in $k$?
closed as off topic by Alex Bartel, Andreas Blass, Felipe Voloch, Gerry Myerson, S. Carnahan♦ Aug 29 2011 at 2:11