Minimal non-FC-groups and coprime automorphisms of quasi-simple groups

Ersoy, Kıvanç
A group G is called an FC-group if the conjugacy class of every element is finite. G is called a minimal non-FC-group if G is not an FC-group, but every proper subgroup of G is an FC-group. The first part of this thesis is on minimal non-FC-groups and their finitary permutational representations. Belyaev proved in 1998 that, every perfect locally finite minimal non-FC-group has non-trivial finitary permutational representation. In Chapter 3, we write the proof of Belyaev in detail. Recall that a group G is called quasi-simple if G is perfect and G/Z(G) is simple. The second part of this thesis is on finite quasi-simple groups and their coprime automorphisms. In Chapter 4, the result of Parker and Quick is written in detail: Namely; if Q is a quasi-simple group and A is a non-trivial group of coprime automorphisms of Q satisfying


Centralizers of finite subgroups in simple locally finite groups
Ersoy, Kıvanç; Kuzucuoğlu, Mahmut; Department of Mathematics (2009)
A group G is called locally finite if every finitely generated subgroup of G is finite. In this thesis we study the centralizers of subgroups in simple locally finite groups. Hartley proved that in a linear simple locally finite group, the fixed point of every semisimple automorphism contains infinitely many elements of distinct prime orders. In the first part of this thesis, centralizers of finite abelian subgroups of linear simple locally finite groups are studied and the following result is proved: If G ...
Divisibility properties on boolean functions using the numerical normal form
Göloğlu, Faruk; Yücel, Melek D; Department of Cryptography (2004)
A Boolean function can be represented in several different forms. These different representation have advantages and disadvantages of their own. The Algebraic Normal Form, truth table, and Walsh spectrum representations are widely studied in literature. In 1999, Claude Carlet and Phillippe Guillot introduced the Numerical Normal Form. NumericalNormal Form(NNF) of a Boolean function is similar to Algebraic Normal Form, with integer coefficients instead of coefficients from the two element field. Using NNF re...
Barely transitive groups
Betin, Cansu; Kuzucuoğlu, Mahmut; Department of Mathematics (2007)
A group G is called a barely transitive group if it acts transitively and faithfully on an infinite set and every orbit of every proper subgroup is finite. A subgroup H of a group G is called a permutable subgroup, if H commutes with every subgroup of G. We showed that if an infinitely generated barely transitive group G has a permutable point stabilizer, then G is locally finite. We proved that if a barely transitive group G has an abelian point stabilizer H, then G is isomorphic to one of the followings: ...
Galois structure of modular forms of even weight
Gurel, E. (Elsevier BV, 2009-10-01)
We calculate the equivariant Euler characteristics of powers of the canonical sheaf on certain modular curves over Z which have a tame action of a finite abelian group. As a consequence, we obtain information on the Galois module structure of modular forms of even weight having Fourier coefficients in certain ideals of rings of cyclotomic algebraic integers. (c) 2009 Elsevier Inc. All rights reserved.
Good action on a finite group
Ercan, Gülin; Jabara, Enrico (Elsevier BV, 2020-10-01)
Let G and A be finite groups with A acting on G by automorphisms. In this paper we introduce the concept of "good action"; namely we say the action of A on G is good, if H = [H, B]C-H (B) for every subgroup B of A and every B-invariant subgroup H of G. This definition allows us to prove a new noncoprime Hall-Higman type theorem.
Citation Formats
K. Ersoy, “Minimal non-FC-groups and coprime automorphisms of quasi-simple groups,” M.S. - Master of Science, Middle East Technical University, 2004.