Algebraic $\overline {\mathbb {Q}}$-Groups as Abstract Groups Paperback / softback
by Olivier Frecon
Part of the Memoirs of the American Mathematical Society series
Paperback / softback
Description
The author analyzes the abstract structure of algebraic groups over an algebraically closed field $K$. For $K$ of characteristic zero and $G$ a given connected affine algebraic $\overline{\mathbb Q}$-group, the main theorem describes all the affine algebraic $\overline{\mathbb Q} $-groups $H$ such that the groups $H(K)$ and $G(K)$ are isomorphic as abstract groups.
In the same time, it is shown that for any two connected algebraic $\overline{\mathbb Q} $-groups $G$ and $H$, the elementary equivalence of the pure groups $G(K)$ and $H(K)$ implies that they are abstractly isomorphic. In the final section, the author applies his results to characterize the connected algebraic groups, all of whose abstract automorphisms are standard, when $K$ is either $\overline {\mathbb Q}$ or of positive characteristic.
In characteristic zero, a fairly general criterion is exhibited.
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Out of Stock - We are unable to provide an estimated availability date for this product
- Format:Paperback / softback
- Pages:99 pages
- Publisher:American Mathematical Society
- Publication Date:30/10/2018
- Category:
- ISBN:9781470429232
Other Formats
- PDF from £70.20
Information
-
Out of Stock - We are unable to provide an estimated availability date for this product
- Format:Paperback / softback
- Pages:99 pages
- Publisher:American Mathematical Society
- Publication Date:30/10/2018
- Category:
- ISBN:9781470429232
