Browsing by Subject "Finite groups."
Now showing 1 - 5 of 5
Results Per Page
Sort Options
Item Open Access Essential cohomology and relative cohomology of finite groups(2009) Aksu, Fatma AltunbulakIn this thesis, we study mod-p essential cohomology of finite p-groups. One of the most important problems on essential cohomology of finite p-groups is finding a group theoretic characterization of p-groups whose essential cohomology is non-zero. This is an open problem introduced in [22]. We relate this problem to relative cohomology. Using relative cohomology with respect to the collection of maximal subgroups of the group, we define relative essential cohomology. We prove that the relative essential cohomology lies in the ideal generated by the essential classes which are the inflations of the essential classes of an elementary abelian p-group. To determine the relative essential cohomology, we calculate the essential cohomology of an elementary abelian p-group. We give a complete treatment of the module structure of it over a certain polynomial subalgebra. Moreover we determine the ideal structure completely. In [17], Carlson conjectures that the essential cohomology of a finite group is finitely generated and is free over a certain polynomial subalgebra. We also prove that Carlson’s conjecture is true for elementary abelian p-groups. Finally, we define inflated essential cohomology and in the case p > 2, we prove that for non-abelian p-groups of exponent p, inflated essential cohomology is zero. This also shows that for those groups, relative essential cohomology is zero. This result gives a partial answer to a particular case of the open problem in [22].Item Open Access Free actions on CW-complexes and varieties of square zero matrices(2011) Şentürk, BerrinGunnar Carlsson stated a conjecture which gives a lower bound on the rank of a differential graded module over a polynomial ring with coefficients in algebraically closed field k when it has a finite dimensional homology over k. Carlsson showed that this conjecture implies the rank conjecture about free actions on product of spheres. In this paper, to understand the Carlsson’s conjecture about differential graded modules, we study the structure of the variety of upper triangular square zero matrices and the techniques which were investigated by Rothbach to determine its irreducible components . We hope these varieties could help prove Carlsson’s conjecture.Item Open Access Obstructions for constructing g-equivariant fibrations(2011) Güçlükan, AslıItem Open Access On lower bounds of character sums(1995) Özbudak, Ferruh111 ilii.s work wo oxlomlod llio ic.sult.s of S.A. Slc|)aiiov [3], [i] about lower bouiid.s for incomplete clia.ra.cter .suiiks over a prime finite Held to the ea..se of arbitrar}^ linite field Moreover we atso a.pplied Cioppats con.struction to .siiperelliptic curves witli a lot of rational |)oints to construct rather good geometric Goppa codes.Item Open Access On lower degree bounds for vector invariants over finite fields(2000) Madran, UğurThe purpose of this thesis is to obtain a lower degree bound in modular invariant theory for a special case. More precisely, let G be any group and k be a finite field of positive characteristic p such that p divides |G| . We prove that if an invariant which has degree at most p —1 with respect to each variable can be written as a polynomial in orbit sums of monomials, then the invariant ring of m copies of the vector space V over k with dimV = n requires a generator of degree ^ ^ ^ provided that m > n where t and rii depends on the representation of G such that |'^'| < t < n + l and 2 < ni < p.