The Permutation Groups - Can Be Expressed,

In this paper we deal with the symmetry group S(f) of a boolean function f on n-variables.The starting of this paper is a false statement in one the theorems of P.Clote and E.Kranakis[2] that every k-representable permutation groups is 2-representable for all k>2. Andrezej Kisielewiezproved that the permutation group -representable but not 2-representable in one the theorems of [3]. We found that there exsits a2- values boolean function on 5 -variables that can represent D.that is, is 2-representable. At last, we show that if a permutation groups isk-representable then is 2-representable;in that, if G is a transfer group then m equals ,else m equals In order to obtain the result, I constructed two more complex boolean functions.