Coset Enumeration in Groups and Constructions of Symmetric Designs

Publisher Summary This chapter discusses coset enumeration in groups and constructions of symmetric designs. It presents a group in terms of generators and relations so that each point or block stabilizer, can be expressed with the same generators. The Coxeter–Todd coset enumeration method with respect to the subgroup gives the number of cosets and also gives the permutation representation of group with respect to the (right) cosets of the subgroup. The corresponding programs have been made by Hrabe De Angelis for each stabilizer subgroup. To construct the design means only to put together all these permutation representations according to the orbit structure matrix. In JANKO–TRAN a symmetric design was constructed whose full automorphism group is discussed.