this paper is dedicated to helmut wielandt on the occasion of his 90th birthday Let A be a transitive subgroup of S n . We show that the largest cyclic quotient of A has order at most n. This can be interpreted as an equivalent result about extensions of constants in the Galois closure of a coverin
Alternating Quotients of Fuchsian Groups
โ Scribed by Brent Everitt
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 235 KB
- Volume
- 223
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
โฆ Synopsis
It is shown that any finitely generated, non-elementary Fuchsian group has among its homomorphic images all but finitely many of the alternating groups A n . This settles in the affirmative a long-standing conjecture of Graham Higman.
๐ SIMILAR VOLUMES
We show that if โซ is a finitely presented normal subgroup of a product G = G 1 2 of Fuchsian groups which projects nontrivially to each factor, then โซ 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
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