Elementary amenable subgroups of R. Thompson's group F

The subgroup structure of Thompson's group F is not yet fully understood. The group F is a subgroup of the group PL(I) of orientation preserving, piecewise linear self homeomorphisms of the unit interval and this larger group thus also has a poorly understood subgroup structure. It is reasonable to guess that F is the "only" subgroup of PL(I) that is not elementary amenable. In this paper, we explore the complexity of the elementary amenable subgroups of F in an attempt to understand the boundary between the elementary amenable subgroups and the non-elementary amenable. We construct an example of an elementary amenable subgroup up to class (height) omega squared, where omega is the first infinite ordinal.Comment: 20 page

Non-noetherian groups without free subgroups and their group algebras (Algebraic system, Logic, Language and Related Areas in Computer Sciences II)

Our interest is in group algebras of non-noetherian groups. In particular, we have studied about primitivity of group algebras and showed that they are often primitive if base groups have non-abelian free subgroups. Our main method includes using two edge-colored graphs. Actually, this method is effective for group algebras of groups with non-abelian free subgroups. On the other hand, there exist some important infinite groups which are non-noetherian but have no non-abelian free subgroups; e.g. Free Burnside groups and the Thompson's group F. In this talk, we first see a brief history on primitivity problem of group algebras of groups with non-abelian free subgroups. Next we introduce Thompson's group F and a problem on group algebras of it. Finally, we improve our graph theory in order to enable to investigate group algebras of Thompson's group F and apply our new graph theory to the problem

R. Thompson's group FF and its group algebras (Logic, Algebraic system, Language and Related Areas in Computer Science)

We have continued to study on group algebras of R. Thompson's group F. We would like to know whether these algebras satisfy the Ore condition or not. This question is directly connected to a well-known problem on F called the amenability problem. Unfortunately we have not been able to reached the answer. On the other hand, recently some research papers on this problem have been published. In this note, we first see a brief introduction for the amenability problem on Thompson's group F and then we consider Cuba's recent results ([4], [6] and [5]) on this problem. Finally, we introduce our approach and the current progress

On group algebras of R. Thompson's group FF (Logic, Language, Algebraic system and Related Areas in Computer Science)

We introduced the amenability problem on R. Thompson's group F and our approach to solve it last year. In this note, we will proceed with the research. We first see a brief introduction for the amenability problem for Thompson's group F and our approach to solving the problem. After that, we introduce Guba's recent results ([7] and [8]) which include a important information for our approach to solve the problem. Finally, we consider what they suggest for our study

Isometry groups of non-positively curved spaces: discrete subgroups

We study lattices in non-positively curved metric spaces. Borel density is established in that setting as well as a form of Mostow rigidity. A converse to the flat torus theorem is provided. Geometric arithmeticity results are obtained after a detour through superrigidity and arithmeticity of abstract lattices. Residual finiteness of lattices is also studied. Riemannian symmetric spaces are characterised amongst CAT(0) spaces admitting lattices in terms of the existence of parabolic isometries.Comment: This is the second of a pair of two articles, originally posted on September 2, 2008 as arXiv:0809.0457v1 For the first part, see arXiv:0809.0457v

Topologische Methoden in der Gruppentheorie

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Contributions to the theory of groups

A 1. The influence on a finite group of its proper abnormal structure. J. London Math. Soc. 40 (1965). 348-61; MR30#4838. • B 2. Abnormal depth and hypereccentric length in finite soluble groups, Math. Z. 90 (1965). 29-40; MR32#141. • C 3. On a splitting theorem of Gaschiitz. Proc. Edinburgh Math. Soc. (20 15 (1966). 57-60; MR33#5708. • A 4. Finite groups with prescribed Sylow tower subgroups. Proc. London Math. Soc. (3) 16 (1966). 577-89; MR33#5734. • B 5. Remarks on system normalizers and Carter subgroups. Proc. Intemat. Conf. Theory of Groups (Canberra I965) (1967). 303-5. • B 6. Finite soluble groups with pronormal system normalizers. Proc. London Math. Soc. (3) 17 (1967). 447-69; MR35#2967. • C 7. A natural setting for the extensions of a group with trivial centre by an arbitrary group. Enseignement Math. 13 (1967). 167-73; MR3871179. • B 8. Nilpotent subgroups of finite soluble groups. Math. Z. 106 (1968). 97-112; MR40#5736. • B 9. Absolutely faithful group actions. Proc. Cambridge Philos. Soc. 66 (1969). 231-7; MR40#1465. • CIO. On the splitting of extensions by a group of prime order. Math. Z. 117 (1970). 239-48; MR43#356. • Cll. Splitting properties of group extensions. Proc. London Math. Soc. (3) 22 (1971). 1-23; MR43#7515. • C12. Extensions by a free abelian group of rank 2. Proc. Roy. Irish Acad. 71A (1971). 19-26. MR44#4097 • BI3. A subnormal embedding theorem for finite groups. J. London Math. Soc. (2) 5 (1972) 253-9; MR47#326. • C14. Universal finite group extensions and a non-splitting theorem. Israel J. Math. 15 (1973) 375-83. • A15. Sufficient conditions for the existence of ordered Sylow towers in finite groups. J. Algebra 28 (1974) 116-26. • Cl6. Automorphism groups of groups with trivial centre. Proc. London Math. Soc. • C17. Frattini normal subgroups of finite groups. unpublished. • A18. On finite insoluble groups with nilpotent maximal subgroups. unpublished

Bosses, Machines, and Urban Voters

Originally published in 1986. Political machines, and the bosses who ran them, are largely a relic of the nineteenth century. A prominent feature in nineteenth-century urban politics, political machines mobilized urban voters by providing services in exchange for voters' support of a party or candidate. Allswang examines four machines and five urban bosses over the course of a century. He argues that efforts to extract a meaningful general theory from the American experience of political machines are difficult given the particularity of each city's history. A city's composition largely determined the character of its political machines. Furthermore, while political machines are often regarded as nondemocratic and corrupt, Allswang discusses the strengths of the urban machine approach—chief among those being its ability to organize voters around specific issues