Commutator and stable commutator lengths in groups



Affine Equivalency and Nonlinearity Preserving Bijective Mappings over F-2
Sertkaya, Isa; Doğanaksoy, Ali; Uzunkol, Osmanbey; Kiraz, Mehmet Sabir (2014-09-28)
We first give a proof of an isomorphism between the group of affine equivalent maps and the automorphism group of Sylvester Hadamard matrices. Secondly, we prove the existence of new nonlinearity preserving bijective mappings without explicit construction. Continuing the study of the group of nonlinearity preserving bijective mappings acting on n-variable Boolean functions, we further give the exact number of those mappings for n <= 6. Moreover, we observe that it is more beneficial to study the automorphis...
Permutation polynomials and construction of bent functions
Ongan, Pınar; Doğanaksoy, Ali; Temür, Burcu Gülmez; Department of Cryptography (2021-3-03)
This thesis consists of two main parts: In the first part, a study of several classes ofpermutation and complete permutation polynomials is given, while in the second part,a method of construction of several new classes of bent functions is described.The first part consists of the study of several classes of binomials and trinomialsover finite fields. A complete list of permutation polynomials of the formf(x) =xqn−1q−1+1+bx∈Fqn[x]is obtained for the casen= 5, and a criterion on permutationpol...
Affine Osserman connections and their Riemann extensions
Garcia-Rio, E; Kupeli, DN; Vazquez-Abal, ME; Vazquez-Lorenzo, R (Elsevier BV, 1999-09-01)
Osserman property is studied for affine torsion-free connections with special attention to the 2-dimensional case. As an application, examples of nonsymmetric and even not locally homogeneous Osserman pseudo-Riemannian metrics are constructed on the cotangent bundle of a manifold equipped with a torsionfree connection by looking at their Riemann extensions. Also, timelike and spacelike Osserman conditions are analyzed for general pseudo-Riemannian manifolds showing that they are equivalent.
Equivariant vector fields on three dimensional representation spheres
Gürağaç, Hami Sercan; Önder, Mustafa Turgut; Department of Mathematics (2011)
Let G be a finite group and V be an orthogonal four-dimensional real representation space of G where the action of G is non-free. We give necessary and sufficient conditions for the existence of a G-equivariant vector field on the representation sphere of V in the cases G is the dihedral group, the generalized quaternion group and the semidihedral group in terms of decomposition of V into irreducible representations. In the case G is abelian, where the solution is already known, we give a more elementary so...
Equivariant CW-complexes and the orbit category
Hambleton, Ian; Pamuk, Semra; YALÇIN, ERGÜN (European Mathematical Society Publishing House, 2013-01-01)
We give a general framework for studying G-CW complexes via the orbit category. As an application we show that the symmetric group G = S-5 admits a finite G-CW complex X homotopy equivalent to a sphere, with cyclic isotropy subgroups.
Citation Formats
M. Korkmaz, “Commutator and stable commutator lengths in groups,” 2019, Accessed: 00, 2021. [Online]. Available: