๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Finitely Presented Normal Subgroups of a Product of Fuchsian Groups

โœ Scribed by F.E.A. Johnson

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
109 KB
Volume
231
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

โœฆ Synopsis

We show that if โŒซ is a finitely presented normal subgroup of a product G = G 1 2

of Fuchsian groups which projects nontrivially to each factor, then โŒซ has finite index in G = G . The proof uses the author's previous reduction of the descrip-1 2 tion of normal subdirect products to the abelian case and an unpublished result of N. C. Carr on the rigidity of normal subdirect products of diagonal rank one.

๐Ÿ“œ SIMILAR VOLUMES

Finite-Rank Free Metabelian Subgroups of
Finite-Rank Free Metabelian Subgroups of Finitely Presented Metabelian Groups
โœ Ada Peluso ๐Ÿ“‚ Article ๐Ÿ“… 1996 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 148 KB

A sufficient condition is obtained for the residual torsion-free nilpotence of certain finitely presented metabelian groups that arise from a matrix representa-ลฝ . tion developed by Magnus 1939, Ann. of Math. 40, 764แŽ768 for metabelian ลฝ groups. Using this condition and a construction due to Baumsla

Free Products in Prime Characteristic: A
Free Products in Prime Characteristic: A Representation of Fuchsian Groups
โœ Stephen D. Cohen; A.M.W. Glass ๐Ÿ“‚ Article ๐Ÿ“… 1996 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 265 KB

In 1988, S. White proved by means of field theory supplemented by a geometric d ลฝ . argument that the real bijections x ยฌ x q 1 and x ยฌ x d an odd prime generate a free group of rank 2. When these maps are considered in prime ลฝ . characteristic p so that x ยฌ x q 1 generates a cyclic group of order p

ON DEFINABILITY OF NORMAL SUBGROUPS OF A
ON DEFINABILITY OF NORMAL SUBGROUPS OF A SUPERSTABLE GROUP
โœ Akito Tsuboi ๐Ÿ“‚ Article ๐Ÿ“… 1992 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 319 KB

## Abstract In this note we treat maximal and minimal normal subgroups of a superstable group and prove that these groups are definable under certain conditions. Main tool is a superstable version of Zil'ber's indecomposability theorem. MSC: 03C60.

Generating Finite Groups with Conjugates
Generating Finite Groups with Conjugates of a Subgroup, II
โœ Paul Flavell ๐Ÿ“‚ Article ๐Ÿ“… 2000 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 298 KB

Suppose that H is a subgroup of a finite group G and that G is generated by the conjugates of H. In this paper, we consider the following question: when can G be generated by two conjugates of H? We began the study of this question in [2]. In order to discuss the results proved in [2] and in this p