For an algebraic curve CรK defined by y 2 =x p +a (a ร K p ) with relative genus ( p&1)ร2 and absolute genus 0, we prove that the Picard group of divisors of degree 0, denoted Pic 0 K (C), of a curve CรK fixed by the action of the Galois group G= gal(K sep รK) has a finite number of K-rational point
Some results on the genus of a group
โ Scribed by Thomas W. Tucker
- Publisher
- John Wiley and Sons
- Year
- 1981
- Tongue
- English
- Weight
- 115 KB
- Volume
- 5
- Category
- Article
- ISSN
- 0364-9024
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โฆ Synopsis
Abstract
This Note announces two results on the genus of a group. First, there is exactly one group of genus two, thus answering a question of V. K. Proulx. Second, the genus of the full symmetric group of degree n is n!/168 + 1, for all n > 167.
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