automorphism group of a possible 2-(115,19,3) symmetric design

let be a set and let be the set of subsets of . the pair in which is a collection of elements of (blocks) is called a design if every element of appears in , times. is called a symmetric design if . in a symmetric design, each element of appears times in blocks of . a mapping between two designs and is an isomorphism if is a one-to-one correspondence and . every isomorphism of a design, , to itself is called an automorphism. the set of all automorphisms of a design with the natural composition rule among mappings forms the automorphism group of the design, and is denoted by . let be an automorphism of a design , we define , and . in this paper we study the automorphism group of a symmetric design with , and prove the following basic theorem. theorem. if is a fixed block of a symmetric design, , which have fixed points, then i) ii) there is a symmetric design in the structure of this design. in the particular case we study the automorphism group of a possible symmetric design. the existence or of a symmetric design is unknown. we prove that theorem. if is a possible symmetric design, then , in which . also if , and i) if , then ii) if , then iii) if , then .