Group actions on Hadamard matrices
نویسنده
چکیده
Faculty of Arts Mathematics Department Master of Literature by Padraig Ó Catháin Hadamard matrices are an important item of study in combinatorial design theory. In this thesis, we explore the theory of cocyclic development of Hadamard matrices in terms of regular group actions on the expanded design. To this end a general theory of both group development and cocyclic development is formulated. This theory is used to classify all regular actions on the expanded designs of Hadamard matrices of order less then 32 that contain a special central involution. We show that such a regular action exists if and only if the matrix is cocyclic. In addition the cocyclic development properties of several Hadamard matrix constructions are reviewed. Some relevant results from the literature are presented, and some non-existence results are given for certain small orders. This work settles some research problems posed by K.J. Horadam in a recent book on Hadamard matrices.
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