04654nam 22013215 450 991015475140332120190708092533.01-4008-8178-110.1515/9781400881789(CKB)3710000000620162(MiAaPQ)EBC4738582(DE-B1597)467981(OCoLC)979970559(DE-B1597)9781400881789(EXLCZ)99371000000062016220190708d2016 fg engurcnu||||||||rdacontentrdamediardacarrierOn Group-Theoretic Decision Problems and Their Classification. (AM-68), Volume 68 /Charles F. MillerPrinceton, NJ : Princeton University Press, [2016]©19721 online resource (121 pages)Annals of Mathematics Studies ;2420-691-08091-7 Includes bibliographical references and index.Frontmatter -- PREFACE -- CONTENTS -- CHAPTER I. INTRODUCTION -- CHAPTER II. PROPERTIES OF BRITTON EXTENSIONS -- CHAPTER III. UNSOLVABILITY RESULTS FOR RESIDUALLY FINITE GROUPS -- CHAPTER IV. THE WORD AND CONJUGACY PROBLEMS FOR CERTAIN ELEMENTARY GROUPS -- CHAPTER V. ON THE ISOMORPHISM PROBLEM FOR GROUPS -- LIST OF REFERENCES -- INDEX OF SYMBOLS -- INDEXPart exposition and part presentation of new results, this monograph deals with that area of mathematics which has both combinatorial group theory and mathematical logic in common. Its main topics are the word problem for groups, the conjugacy problem for groups, and the isomorphism problem for groups. The presentation depends on previous results of J. L. Britton, which, with other factual background, are treated in detail.Annals of mathematics studies ;Number 68.Group theoryLogic, Symbolic and mathematicalAbelian group.Betti number.Characteristic function (probability theory).Characterization (mathematics).Combinatorial group theory.Conjecture.Conjugacy class.Conjugacy problem.Contradiction.Corollary.Cyclic permutation.Decision problem.Diffeomorphism.Direct product.Direct proof.Effective method.Elementary class.Embedding.Enumeration.Epimorphism.Equation.Equivalence relation.Exact sequence.Existential quantification.Finite group.Finite set.Finitely generated group.Finitely presented.Free group.Free product.Fundamental group.Fundamental theorem.Group (mathematics).Group theory.Gödel numbering.Homomorphism.Homotopy.Inner automorphism.Markov property.Mathematical logic.Mathematical proof.Mathematics.Monograph.Natural number.Nilpotent group.Normal subgroup.Notation.Permutation.Polycyclic group.Presentation of a group.Quotient group.Recursive set.Requirement.Residually finite group.Semigroup.Simple set.Simplicial complex.Solvable group.Statistical hypothesis testing.Subgroup.Theorem.Theory.Topology.Transitive relation.Triviality (mathematics).Truth table.Turing degree.Turing machine.Without loss of generality.Word problem (mathematics).Group theory.Logic, Symbolic and mathematical.512/.2Miller Charles F., 55992DE-B1597DE-B1597BOOK9910154751403321On Group-Theoretic Decision Problems and Their Classification. (AM-68), Volume 682787933UNINA