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010 a| 2022022770;

020 a| 9781470451196q| (paperback);

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035 a| (WaSeSS)ssib047879109;

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100 1 a| Craven, David A.?| UNAUTHORIZED;

245 10 a| Maximal PSL2 subgroups of exceptional groups of lie typeh| [electronic resource] /c| David A. Craven.;

260 a| Providence, RI :b| AMS, American Mathematical Society,c| 2022.;

300 a| v, 155 pages :b| illustrations ;c| 26 cm;

490 0 a| Memoirs of the American Mathematical Society,x| 0065-9266 ;v| number 1355;

504 a| Includes bibliographical references.;

505 0 a| Notation and preliminaries -- Maximal subgroups -- Maximal subgroups and subspace stabilizers -- Blueprint theorems for semisimple elements -- Unipotent and semisimple elements -- Modules for SL2 -- Some PSL2s inside E6 in characteristic -- Proof of the theorems : strategy -- The proof for F4 -- The proof for E6 -- The proof for E7 in characteristic -- The proof for E7 in odd characteristic : PSL2 embedding -- The proof for E7 in odd characteristic : SL2 embedding.;

506 a| Available only to authorized users.;

520 a| "We study embeddings of PSL2(pa) into exceptional groups G(pb) for G = F4, E6, 2E6, E7, and p a prime with a, b positive integers. With a few possible exceptions, we prove that any almost simple group with socle PSL2(pa), that is maximal inside an almost simple exceptional group of Lie type F44, E6, 2E6 and E7, is the fixed points under the Frobenius map of a corresponding maximal closed subgroup of type A1 inside the algebraic group. Together with a recent result of Burness and Testerman for p the Coxeter number plus one, this proves that all maximal subgroups with socle PSL2(pa) inside these finite almost simple groups are known, with three possible exceptions (pa = 7, 8, 25 for E7). In the three remaining cases we provide considerable information about a potential maximal subgroup"--c| Provided by publisher.;

538 a| Mode of access: World Wide Web;

650 0 a| Lie groups.=| ^A17435;

650 0 a| Maximal subgroups.=| ^A213501;

650 0 a| Exceptional Lie algebras.=| ^A109024;

650 7 a| Group theory and generalizations -- Abstract finite groups -- Simple groups: alternating groups and groups of Lie type.2| msc;

650 7 a| Group theory and generalizations -- Linear algebraic groups and related topics -- Exceptional groups.2| msc;

655 0 a| Electronic books.=| ^A491897;

856 40 z| Full text available from Ebook Central - Academic Completeu| https://ebookcentral.proquest.com/lib/eastcarolina/detail.action?docID=6939728;

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Maximal PSL2 subgroups of exceptional groups of lie type / David A. Craven.

Author/creator	Craven, David A.
Format	Electronic
Publication Info	Providence, RI : AMS, American Mathematical Society, 2022.
Description	v, 155 pages : illustrations ; 26 cm
Supplemental Content	Full text available from Ebook Central - Academic Complete
Subjects	Lie groups. Maximal subgroups. Exceptional Lie algebras.

Series	Memoirs of the American Mathematical Society, 0065-9266 ; number 1355
Contents	Notation and preliminaries -- Maximal subgroups -- Maximal subgroups and subspace stabilizers -- Blueprint theorems for semisimple elements -- Unipotent and semisimple elements -- Modules for SL2 -- Some PSL2s inside E6 in characteristic -- Proof of the theorems : strategy -- The proof for F4 -- The proof for E6 -- The proof for E7 in characteristic -- The proof for E7 in odd characteristic : PSL2 embedding -- The proof for E7 in odd characteristic : SL2 embedding.
Abstract	"We study embeddings of PSL2(pa) into exceptional groups G(pb) for G = F4, E6, 2E6, E7, and p a prime with a, b positive integers. With a few possible exceptions, we prove that any almost simple group with socle PSL2(pa), that is maximal inside an almost simple exceptional group of Lie type F44, E6, 2E6 and E7, is the fixed points under the Frobenius map of a corresponding maximal closed subgroup of type A1 inside the algebraic group. Together with a recent result of Burness and Testerman for p the Coxeter number plus one, this proves that all maximal subgroups with socle PSL2(pa) inside these finite almost simple groups are known, with three possible exceptions (pa = 7, 8, 25 for E7). In the three remaining cases we provide considerable information about a potential maximal subgroup"-- Provided by publisher.
Bibliography note	Includes bibliographical references.
Access restriction	Available only to authorized users.
Technical details	Mode of access: World Wide Web
Genre/form	Electronic books.
LCCN	2022022770
ISBN	9781470451196 (paperback)
ISBN	(pdf)

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Maximal PSL2 subgroups of exceptional groups of lie type / David A. Craven.

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