Algebraic $\overline {\mathbb {Q}}$-Groups as Abstract Groups

Algebraic $\overline {\mathbb {Q}}$-Groups as Abstract Groups
Author :
Publisher : American Mathematical Soc.
Total Pages : 112
Release :
ISBN-10 : 9781470429232
ISBN-13 : 1470429233
Rating : 4/5 (32 Downloads)

Book Synopsis Algebraic $\overline {\mathbb {Q}}$-Groups as Abstract Groups by : Olivier Frécon

Download or read book Algebraic $\overline {\mathbb {Q}}$-Groups as Abstract Groups written by Olivier Frécon and published by American Mathematical Soc.. This book was released on 2018-10-03 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author analyzes the abstract structure of algebraic groups over an algebraically closed field . For of characteristic zero and a given connected affine algebraic Q -group, the main theorem describes all the affine algebraic Q -groups such that the groups and are isomorphic as abstract groups. In the same time, it is shown that for any two connected algebraic Q -groups and , the elementary equivalence of the pure groups and 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 is either Q or of positive characteristic. In characteristic zero, a fairly general criterion is exhibited.


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