LEADER 03640nam 2200529 450 001 9910793296603321 005 20220525075748.0 010 $a1-4704-4815-7 035 $a(CKB)4100000007133848 035 $a(MiAaPQ)EBC5571101 035 $a(Au-PeEL)EBL5571101 035 $a(OCoLC)1065073359 035 $a(RPAM)20662073 035 $a(PPN)231946023 035 $a(EXLCZ)994100000007133848 100 $a20220525d2018 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAlgebraic Q-groups as abstract groups /$fOlivier Fre?con 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d[2018] 210 4$d©2018 215 $a1 online resource (v, 99 pages) 225 1 $aMemoirs of the American Mathematical Society ;$vNumber 1219 300 $a"September 2018 . Volume 255 . Number 1219 (second of 7 numbers)." 311 $a1-4704-2923-3 320 $aIncludes bibliographical references and index. 327 $aCover -- Title page -- Chapter 1. Introduction -- 1.1. Related work -- 1.2. The field of definition -- 1.3. Overview of the paper -- Chapter 2. Background material -- 2.1. Groups of finite Morley rank -- 2.2. Fundamental theorems -- 2.3. Decent tori and pseudo-tori -- 2.4. Unipotence -- Chapter 3. Expanded pure groups -- Chapter 4. Unipotent groups over \ov{\Q} and definable linearity -- Chapter 5. Definably affine groups -- 5.1. Definition and generalities -- 5.2. The subgroup ( ) -- 5.3. The subgroup ( ) -- Chapter 6. Tori in expanded pure groups -- Chapter 7. The definably linear quotients of an -group -- 7.1. The subgroups ( ) and ( ) -- 7.2. The nilpotence of ( ) -- 7.3. The subgroup ( ) when the ground field is \ov{\Q} -- 7.4. The subgroups ( ) and ( ) in positive characteristic -- Chapter 8. The group _{ } and the Main Theorem for =\ov{\Q} -- Chapter 9. The Main Theorem for =?\ov{\Q} -- Chapter 10. Bi-interpretability and standard isomorphisms -- 10.1. Positive characteristic and bi-interpretability -- 10.2. Characteristic zero -- Acknowledgements -- Bibliography -- Index of notations -- Index -- Back Cover. 330 $aThe author analyzes the abstract structure of algebraic groups over an algebraically closed field K. For K of characteristic zero and G a given connected affine algebraic \overline{\mathbb Q}-group, the main theorem describes all the affine algebraic \overline{\mathbb Q} -groups H such that the groups H(K) and G(K) are isomorphic as abstract groups. In the same time, it is shown that for any two connected algebraic \overline{\mathbb Q} -groups G and H, the elementary equivalence of the pure groups G(K) and H(K) implies that they are abstractly isomorphic. In the final section, the author applies his results to characterize the connected algebraic groups, all of whose abstract automorphisms are standard, when K is either \overline {\mathbb Q} or of positive characteristic. In characteristic zero, a fairly general criterion is exhibited. 410 0$aMemoirs of the American Mathematical Society ;$vNumber 1219. 606 $aAlgebra 606 $aFinite groups 606 $aIsomorphisms (Mathematics) 615 0$aAlgebra. 615 0$aFinite groups. 615 0$aIsomorphisms (Mathematics) 676 $a512.9 700 $aFre?con$b Olivier$f1974-$01544050 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910793296603321 996 $aAlgebraic Q-groups as abstract groups$93797936 997 $aUNINA LEADER 01272nam0 22002651i 450 001 UON00299763 005 20231205103958.911 100 $a20070725d1963 |0itac50 ba 101 $aeng 102 $aGB 105 $a|||| 1|||| 200 1 $aˆA ‰bibliography of the writings in verse and prose of George Gordon Noel, baron Byron, with letters illustrating his life and work and particularly his attitude towards Keats$fby Thomas James Wise 210 $aLondon$cDawson of Pall Mall$d1963 215 $a2 v.$d25 cm. 606 $aBYRON GEORGE GORDON$3UONC042214$2FI 620 $aGB$dLondon$3UONL003044 676 $a821.7$cPoesia inglese. 1800-1837$v21 700 1$aWISE$bThomas James$3UONV172453$0394661 712 $aDawsons of Pall Mall$3UONV251738$4650 801 $aIT$bSOL$c20240220$gRICA 899 $aSIBA - SISTEMA BIBLIOTECARIO DI ATENEO$2UONSI 912 $aUON00299763 950 $aSIBA - SISTEMA BIBLIOTECARIO DI ATENEO$dSI Angl IV B BYR WIS 1-2 $eSI SI 2164 5 1-2 996 $aBibliography of the writings in verse and prose of George Gordon Noel, baron Byron, with letters illustrating his life and work and particularly his attitude towards Keats$91380706 997 $aUNIOR