Automorphism Group of a Possible 2-(121, 16, 2) Symmetric Design

Let 0 be a symmetric 2-( 121, 16, 2) design with the automorphism group ofaut(d). in this paper the order of automorphism of prime order of aut(d) isstudied, and some results are obtained about the number of fixed points of theseautomorphisms, also we will show that iaut(d)i==2p 3q sf 75 u 13u, where p, q, r,s, t and u are non-negative integers such that r, s, t, u :s 1. in addition we presentsome general results on the automorphisms with prime order of a symmetricdesign and some general results on the automorphism groups of a symmetricdesign are given and in section 3, we prove a series of lemma. based on them wecan prove main theorem. one of the reasons for the emergence and growth ofblock designs is the combined irrigation of fields having a lot of patches, at theend of the paper, there is offered an application of block design in modemirrigation.