engleski

Construction of block designs admitting a solvable automorphism group

In this talk we will describe a method for the construction of block designs admitting a solvable automorphism group using tactical decomposition. The first step is the construction of mutually nonisomorphic orbit matrices for arbitrary block design and its persumed automorphism group, which is a generalisation of the algorithm for obtaining orbit matrices for some symmetric design and its automorphism group. The second step in the construction is often called indexing of orbit matrices, which is construction of block designs from orbit matrices. Indexing often lasts too long, therefore we develop an algorithm for the refinement of orbit matrices, based on the application of the composition series for a solvable automorphism group which acts on a block design. We have applied the mentioned method for the construction of some new block designs admitting a solvable automorphism group.

Block design ; Tactical decomposition of design ; orbit matrix ; Automorphism group, Refinement of orbit matrices ; Composition series

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