02866cam  22003978i 450000100090000000300050000900500170001400600190003100700150005000800410006502000270010604000370013305000230017008200150019310000380020824500860024626300090033226400600034130000340040133600260043533700280046133800270048949000740051650000710059050505100066150600500117152007800122150400510200153300950205253800360214758800470218365000140223077601320224485600440237685600480242020662073RPAM20180920153557.0m      b    001 0 cr/|||||||||||180920s2018    riu     ob    001 0 eng c  a9781470448158 (online)  aLBSOR/DLCbengerdacLBSORdRPAM00aQA174.2b.F74 201800a512/.22231 aFrâecon, Olivier,d1974-eauthor.10aAlgebraic Q-groups as abstract groups /h[electronic resource] cOlivier Frâecon.  a1809 1aProvidence, RI :bAmerican Mathematical Society,c2018.  a1 online resource (pages cm.)  atextbtxt2rdacontent  aunmediatedbn2rdamedia  avolumebnc2rdacarrier0 aMemoirs of the American Mathematical Society, x1947-6221 ; vv. 1219  a"September 2018 . Volume 255 . Number 1219 (second of 7 numbers)."00tChapter 1. IntroductiontChapter 2. Background materialtChapter 3. Expanded pure groupstChapter 4. Unipotent groups over $\ov \Q $ and definable linearitytChapter 5. Definably affine groupstChapter 6. Tori in expanded pure groupstChapter 7. The definably linear quotients of an $ACF$-grouptChapter 8. The group $D_G$ and the Main Theorem for $K=\ov \Q $tChapter 9. The Main Theorem for $K\neq \ov \Q $tChapter 10. Bi-interpretability and standard isomorphismstAcknowledgementstIndex of notations1 aAccess is restricted to licensed institutions  a"We analyze the abstract structure of algebraic groups over an algebraically closed field K. For K of characteristic zero and G a given connected affine algebraic Q-group, the main theorem describes all the affine algebraic 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 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 chapter, we apply our results to characterize the connected algebraic groups all of whose abstract automorphisms are standard, when K is either Q or of positive characteristic. In characteristic zero, a fairly general criterion is exhibited"--cProvided by publisher.  aIncludes bibliographical references and index.  aElectronic reproduction.bProvidence, Rhode Island :cAmerican Mathematical Society.d2018  aMode of access : World Wide Web  aDescription based on print version record. 0aQ-groups.0 iPrint version: aFrâecon, Olivier, 1974-tAlgebraic Q-groups as abstract groups /w(DLC)   2018040526x0065-9266z97814704292324 3Contentsuhttp://www.ams.org/memo/1219/4 3Contentsuhttps://doi.org/10.1090/memo/1219