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OverviewThe 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. Full Product DetailsAuthor: Olivier FreconPublisher: American Mathematical Society Imprint: American Mathematical Society Weight: 0.175kg ISBN: 9781470429232ISBN 10: 1470429233 Pages: 99 Publication Date: 30 October 2018 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Temporarily unavailable The supplier advises that this item is temporarily unavailable. It will be ordered for you and placed on backorder. Once it does come back in stock, we will ship it out to you. Table of ContentsReviewsAuthor InformationOlivier Frecon, Laboratoire de Mathematiques et Applications, Universite de Poitiers, France. Tab Content 6Author Website:Countries AvailableAll regions |