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# Department of Mathematics

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### Browsing Department of Mathematics by Subject "13A50"

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Item Open Access Degree of reductivity of a modular representation(World Scientific Publishing, 2017) Kohls, M.; Sezer, M.Show more For a finite-dimensional representation V of a group G over a field F, the degree of reductivity δ(G,V) is the smallest degree d such that every nonzero fixed point υ ∈ VG/{0} can be separated from zero by a homogeneous invariant of degree at most d. We compute δ(G,V) explicitly for several classes of modular groups and representations. We also demonstrate that the maximal size of a cyclic subgroup is a sharp lower bound for this number in the case of modular abelian p-groups. © 2017 World Scientific Publishing Company.Show more Item Open Access Hilbert ideals of vector invariants of s2 and S3(Heldermann Verlag, 2012) Sezer, M.; Ünlü, Ö.Show more The Hilbert ideal is the ideal generated by positive degree invariants of a finite group. We consider the vector invariants of the natural action of S n . For S 2 we compute the reduced and universal Gröbner bases for the Hilbert ideal. As well, we identify all initial form ideals of the Hilbert ideal and describe its Gröbner fan. In modular characteristics, we show that the Hilbert ideal for S 3 can be generated by polynomials of degree at most three and the reduced Gröbner basis contains no polynomials that involve variables from four or more copies. Our results give support for conjectures for improved degree bounds and regularity conditions on the Gröbner bases for the Hilbert ideal of vector invariants of S n. © 2012 Heldermann Verlag.Show more Item Open Access Separating invariants for the klein four group and cyclic groups(World Scientific Publishing, 2013-06-11) Kohls, M.; Sezer, M.Show more We consider indecomposable representations of the Klein four group over a field of characteristic 2 and of a cyclic group of order pm with p, m coprime over a field of characteristic p. For each representation, we explicitly describe a separating set in the corresponding ring of invariants. Our construction is recursive and the separating sets we obtain consist of almost entirely orbit sums and products. © 2013 World Scientific Publishing CompanyShow more