Barely transitive groups

Betin, Cansu
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: (i) G is a metabelian locally finite p-group, (ii) G is a finitely generated quasi-finite group (in particular H is finite), (iii) G is a finitely generated group with a maximal normal subgroup N where N is a locally finite metabelian group. In particular, G=N is a quasi-finite simple group. In all of the three cases, G is periodic.


Minimal non-FC-groups and coprime automorphisms of quasi-simple groups
Ersoy, Kıvanç; Kuzucuoğlu, Mahmut; Department of Mathematics (2004)
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 ...
Monomial groups
Almaş, Özge; Kuzucuoğlu, Mahmut; Solak, Ebru; Department of Mathematics (2017)
A group G is called a permutation group if it is a subgroup of a symmetric group on aset Ω. GiscalledalineargroupifitisasubgroupofthegenerallineargroupGL(n, F) for a field F. Monomial groups are generalization of permutation groups and restriction of linear groups. In matrix terminology, monomial groups of degree n over a group H are the n× n invertible matrices in which each row and each column contains only one element of H all the other entries are zero. Basic properties of finite degree monomial groups ar...
Measurement of the t(t)over-bar production cross section in pp collisions at root s=7 TeV in dilepton final states containing a tau
Chatrchyan, S.; et. al. (2012-06-01)
The top quark pair production cross section is measured in dilepton events with one electron or muon, and one hadronically decaying tau lepton from the decay t (t) over bar -> (l nu(l))((sic)(h)nu((sic)))b (b) over bar, (l = e, mu). The data sample corresponds to an integrated luminosity of 2.0 fb(-1) for the electron channel and 2.2 fb(-1) for the muon channel, collected by the CMS detector at the LHC. This is the first measurement of the t (t) over bar cross section explicitly including tau leptons in pro...
The classical involution theorem for groups of finite Morley rank
Berkman, A (Elsevier BV, 2001-09-15)
This paper gives a partial answer to the Cherlin-Zil'ber Conjecture, which states that every infinite simple group of finite Morley rank is isomorphic to an algebraic group over an algebraically closed field. The classification of the generic case of tame groups of odd type follows from the main result of this work, which is an analogue of Aschbacher's Classical Involution Theorem for finite simple groups. (C) 2001 Academic Press.
Özbudak, Ferruh (Informa UK Limited, 2014-09-02)
Let F-q be an arbitrary finite field of characteristic 2 and k be an arbitrary even integer. We count the number of quadratic forms having codimension 2 radicals on F-q(k) over F-q such that the corresponding curve is maximal or minimal. This problem is first attempted in [3], in which the number of maximal curves is obtained only for (q, k) = (2, 6) and (q, k) = (2, 8).
Citation Formats
C. Betin, “Barely transitive groups,” Ph.D. - Doctoral Program, Middle East Technical University, 2007.