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National Repository of Grey Literature 2 records found  Search took 0.00 seconds. 
Local-global principle for quadratic forms
 Surý, Pavel ; Kala, Vítězslav (advisor) ; Vávra, Tomáš (referee)
Local-global principle for quadratic forms This work will be focused on the problems of representation and equivalence for quadratic forms. We will prove the fundamental Hasse-Minkowski theorem, which describes the rational representation and equivalence using properties of the form over the completions of Q: the real and p-adic numbers. We will refer to this procedure as local-global principle. Furthermore, we shall describe the methods for computing the p-adic invariants, and show their relation to the representation problem. Finally, we show how the local-global partially extends to integral forms, in particular to indefinite ones of dimension at least 4. 1
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Highly transitive groups
 Surý, Pavel ; Stanovský, David (advisor) ; Příhoda, Pavel (referee)
Highly transitive groups We say that a group action is 5-transitive, if for every two 5-tuples of distinct points there is a group action mapping one of the tuples to the other one. In this thesis, we will construct W12 and W24 Steiner systems as three-point extensions of the affine plane AG2(3) and the projective plane PG2(4). We will conclude that the automorphism groups of the systems, so called Mathieu groups M12 and M24, are 5-transitive. 1
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