05023nam 22006253 450 991097091550332120231110223426.097814704722901470472295(MiAaPQ)EBC29731927(Au-PeEL)EBL29731927(CKB)24767778700041(OCoLC)1343248790(PPN)270358773(EXLCZ)992476777870004120220904d2022 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierFactorizations of Almost Simple Groups with a Solvable Factor, and Cayley Graphs of Solvable Groups1st ed.Providence :American Mathematical Society,2022.©2022.1 online resource (112 pages)Memoirs of the American Mathematical Society ;v.279Print version: Li, Cai-Heng Factorizations of Almost Simple Groups with a Solvable Factor, and Cayley Graphs of Solvable Groups Providence : American Mathematical Society,c2022 9781470453831 Cover -- Title page -- Chapter 1. Introduction -- 1.1. Factorizations of almost simple groups -- 1.2. -Arc-transitive Cayley graphs -- 1.3. Discussions and some open problems -- Chapter 2. Preliminaries -- 2.1. Notation -- 2.2. Results on finite simple groups -- 2.3. Elementary facts concerning factorizations -- 2.4. Maximal factorizations of almost simple groups -- Chapter 3. The factorizations of linear and unitary groups of prime dimension -- 3.1. Singer cycles -- 3.2. Linear groups of prime dimension -- 3.3. Unitary groups of prime dimension -- Chapter 4. Non-classical groups -- 4.1. The case that both factors are solvable -- 4.2. Exceptional groups of Lie type -- 4.3. Alternating group socles -- 4.4. Sporadic group socles -- Chapter 5. Examples in classical groups -- 5.1. Examples in unitary groups -- 5.2. Examples in symplectic groups -- 5.3. Examples in orthogonal groups of odd dimension -- 5.4. Examples in orthogonal groups of plus type -- Chapter 6. Reduction for classical groups -- 6.1. Inductive hypothesis -- 6.2. The case that has at least two non-solvable composition factors -- Chapter 7. Proof of Theorem 1.1 -- 7.1. Linear groups -- 7.2. Symplectic Groups -- 7.3. Unitary Groups -- 7.4. Orthogonal groups of odd dimension -- 7.5. Orthogonal groups of even dimension -- 7.6. Completion of the proof -- Chapter 8. -Arc-transitive Cayley graphs of solvable groups -- 8.1. Preliminaries -- 8.2. A property of finite simple groups -- 8.3. Reduction to affine and almost simple groups -- 8.4. Proof of Theorem 1.3 and Corollary 1.5 -- Appendix A. Tables for nontrivial maximal factorizations of almost simple classical groups -- Bibliography -- Back Cover."A characterization is given for the factorizations of almost simple groups with a solvable factor. It turns out that there are only several infinite families of these nontrivial factorizations, and an almost simple group with such a factorization cannot have socle exceptional Lie type or orthogonal of minus type. The characterization is then applied to study s-arc-transitive Cayley graphs of solvable groups, leading to a striking corollary that, except for cycles, a non-bipartite connected 3-arc-transitive Cayley graph of a finite solvable group is necessarily a normal cover of the Petersen graph or the Hoffman-Singleton graph"--Provided by publisher.Memoirs of the American Mathematical Society Finite groupsGroup theoryGroup theory and generalizations -- Abstract finite groups -- Products of subgroupsmscGroup theory and generalizations -- Abstract finite groups -- Simple groups: alternating groups and groups of Lie typemscGroup theory and generalizations -- Abstract finite groups -- Simple groups: sporadic groupsmscCombinatorics -- Algebraic combinatorics -- Group actions on combinatorial structuresmscFinite groups.Group theory.Group theory and generalizations -- Abstract finite groups -- Products of subgroups.Group theory and generalizations -- Abstract finite groups -- Simple groups: alternating groups and groups of Lie type.Group theory and generalizations -- Abstract finite groups -- Simple groups: sporadic groups.Combinatorics -- Algebraic combinatorics -- Group actions on combinatorial structures.512/.23512.2320D4020D0620D0805E18mscLi Cai-Heng1801534Xia Binzhou1801535MiAaPQMiAaPQMiAaPQBOOK9910970915503321Factorizations of Almost Simple Groups with a Solvable Factor, and Cayley Graphs of Solvable Groups4346814UNINA01731nam0 2200433 i 450 VAN0005011120250613085008.408978-03-87944-22-720060824d1995 |0itac50 baengUS|||| |||||i e nncApplied Functional AnalysisMain Principles and Their ApplicationsEberhard ZeidlerNew YorkSpringer1995xvi, 404 p.ill.25 cm001VAN000237172001 Applied mathematical sciences210 Berlin [etc]Springer1971-10946-XXFunctional analysis [MSC 2020]VANC019764MF47-XXOperator theory [MSC 2020]VANC019759MF81-XXQuantum theory [MSC 2020]VANC019967MFCalculusKW:KCalculus of variationsKW:KFunctional AnalysisKW:KGame TheoryKW:KHilbert spacesKW:KOptimal ControlKW:KOptimizationKW:KUSNew YorkVANL000011ZeidlerEberhardVANV02632040565Springer <editore>VANV108073650ITSOL20250620RICA/sebina/repository/catalogazione/documenti/Zeidler - Applied functional analysis...main principles....pdfContentsBIBLIOTECA DEL DIPARTIMENTO DI MATEMATICA E FISICAIT-CE0120VAN08VAN00050111BIBLIOTECA DEL DIPARTIMENTO DI MATEMATICA E FISICA08PREST 46-XX 4969 08 6009 I 20060824 Applied functional analysis83422UNICAMPANIA