2 edition of **On group-theoretic decision problems and their classification.** found in the catalog.

On group-theoretic decision problems and their classification.

Charles F. Miller

- 296 Want to read
- 26 Currently reading

Published
**1971** by Princeton University Press in Princeton, N.J .

Written in English

- Groups, Theory of,
- Logic, Symbolic and mathematical

**Edition Notes**

Series | Annals of mathematics studies, no. 68 |

The Physical Object | |
---|---|

Pagination | 106p. |

Number of Pages | 106 |

ID Numbers | |

Open Library | OL14804885M |

This book is about relations between three different areas of mathematics and theoretical computer science: combinatorial group theory, cryptography, and complexity theory. It is explored how non-commutative (infinite) groups, which are typically studied in combinatorial group theory, can be used in public key cryptography. Logic Godel's incompleteness theorems GodSl provided undecidable statements in sense 1 for a wide variety of axiom systems. Inspired by this, Church and Turing began to prove that certain decision problems were undecidable in sense 2, as soon as they developed their . On group-theoretic decision problems and their classification: Miller Charles F. University Press - Princeton: Theory and applications of finite groups: MILLER G. A. BLICHFELDT H. F. DICKSON L. E. G. E. Stechert & Co. - New York: Probabilidad y estad¡stica para ingenieros: MILLER Irwin R. FREUND John E. JOHNSON Richard. The article The Abstract Group Concept, from the McTutor archive, gives an accounting of the steps towards the modern abstract brief, Cayley made the first stumbling attempts (citing the associative law explicitly) in an paper, but not until did Weber give the modern definition, in his Lehrbuch der included infinite groups.

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In [1] Britton gives a “group-theoretic” proof of the unsolvability of the word problem for finitely presented groups. His proof uses a very powerful result [16, Lemma 4 (the principal lemma)] on presentations which has become known asBritton’s Lemmaand has since been used by several other the appendix to [16] Britton states a generalization of this lemma asTheorem A.

On Group-Theoretic Decision Problems and Their Classification. (AM), Volume 68 - Ebook written by Charles F. Miller III. Read this book using Google Play Books app on your PC, android, iOS devices.

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(Annals of Mathematics Studies, No. 68) on FREE SHIPPING on qualified ordersCited by: the word and conjugacy problems for certain elementary groups, pg. 45*chapter v. on the isomorphism problem for groups, pg. 79*list of references, pg. 97*index of symbols, pg. *index, pg. Series Title.

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Buy On Group-Theoretic Decision Problems and Their Classification. (AM), Volume 68 ebooks from by Miller, Charles F. from Princeton University Press published on 3/2/ Use our personal learning platform and check out our low prices and other ebook categories.

Books 1. On Group-Theoretic Decision Problems and Their Classification. (AM), Volume 68 Charles F. Miller III. Part exposition and part presentation of new results, this On group-theoretic decision problems and their classification.

book deals with that area of mathematics which has both combinatorial group theory and mathematical logic in common. Miller III, “On group theoretic decision problems and their classification”, Annals of Math. On group-theoretic decision problems and their classification.

book St Princeton University Press, Princeton, NJ, Google ScholarCited by: The Classical Groups: Their Invariants and Representations (PMS-1) - Ebook written by Hermann Weyl. Read this book using Google Play Books app on your PC, android, iOS devices. Download for offline reading, highlight, bookmark or take notes while you read The Classical Groups: Their Invariants and Representations (PMS-1).Author: Hermann Weyl.

C.F. Miller IIIOn Group-theoretic Decision Problems and their Classification Ann. of Math. Stud., 68, Princeton University Press, Princeton, NJ () Google ScholarCited by: Part of the Lecture Notes in Mathematics book series (LNM, volume C.

Miller, III, On group-theoretic decision problems and their classification, Annals of Math. There are no affiliations available. About this paper. Cite this paper as: Gersten S.M. () Problems about higher K-functors.

In: Bass H. (eds) Higher K-Theories. Cited by: In mathematics and abstract algebra, group theory studies the algebraic structures known as concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as groups endowed with additional operations and recur throughout mathematics, and the methods of group theory have influenced many.

On group-theoretic decision problems and their classification [14] C. Miller III, Decision problems for groups: survey and reflections -in Algorithms and Classification in Combinatorial Group.

On Group-Theoretic Decision Problems and Their Classification. (AM) On Knots. (AM) On the Cohomology of Certain Non-Compact Shimura Varieties (AM) On the Tangent Space to the Space of Algebraic Cycles on a Smooth Algebraic Variety.

(AM) Advancing research. Creating by: 3. Charles F. Miller III, On group-theoretic decision problems and their classification, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, Annals of Mathematics Studies, No.

MR ; Robert Myers, Open book decompositions of 3 Recursive unsolvability of group theoretic problems, Ann. On Group-Theoretic Decision Problems and Their Classification. (AM) by Miller, Charles F., III Part 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. Group-theoretic synonyms, Group-theoretic pronunciation, Group-theoretic translation, English dictionary definition of Group-theoretic.

The branch of mathematics concerned. It turns out that most classic group-theoretic decision problems, such as the word, conjugacy, membership and the isomorphism problems, have provably low complexity on " random " inputs even if.

Roger C. Lyndon and Paul Schupp, Geometric group theor], (tentative title), Ergebnisse der Mathematik (Springer, Berlin, to appear). Charles F. Miller,On group-theoretic decision p r o b l e m and their classification, Annals of Mathematic Studies (Princeton Univ.

Press, Princeton, N.J., ). On Group-Theoretic Decision Problems and Their Classification. (AM), Volume 68 Charles F. Miller III. Part 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. On Group-Theoretic Decision Problems and Their Classification: QAM48 #68 Details: Morris W. & Mazur, Barry Hirsch; Morris W. Hirsch; Barry Mazur; Morris W Hirsch: Smoothings of Piecewise Linear Manifolds. (AM) (Annals of Mathematics Studies Series) QAH Details.

Numerical Methods for Solving Inverse Problems of Mathematical Physics: Numerical Particle-in-Cell Methods: On Group-Theoretic Decision Problems and Their Classification. (AM), Volume On Knots. (AM), Volume On the Cohomology of Certain Non-Compact Shimura Varieties (AM.

Infinite groups are also considered, with particular attention to logical and decision problems. Abelian, nilpotent and solvable groups are studied both in the finite and infinite case. Permutation groups and are treated in detail; their relationship with Galois theory is often taken into : Springer-Verlag Mailand.

The algorithmic unsolvability of the conjugacy problem for finitely presented groups was demonstrated by Novikov in the early s. Various simplifications and alternative proofs were found by lat Cited by: 3. Two Theorems about Nilpotent Subgroup Lijiang Zeng. Department of Mathematics, Zunyi Normal College, Zunyi, China and proved two interesting theorems about nilpotent subgroup in these properties.

“On Group Theoretic Decision Problems and File Size: KB. Bulletin of the London Mathematical Society; Journal of the London Mathematical Society; Book reviews. COHOMOLOGICAL METHODS IN GROUP THEORY. Cohen; ON GROUP‐THEORETIC DECISION PROBLEMS AND THEIR CLASSIFICATION. Clapham; Pages: ; First Published: March.

This is the second in a planned series of papers in which musical scales, tuning, and temperament are studied from a mathematical point of view.(1) In the present paper, group-theoretic methods are used to study N-tone scales for various N. Explore books by Charles F. Miller with our selection at Click and Collect from your local Waterstones or get FREE UK delivery on orders over £ Group-Theoretic Methods in Mechanics and Applied Mathematics - CRC Press Book Group analysis of differential equations has applications to various problems in nonlinear mechanics and physics.

For the first time, this book gives the systematic group analysis of main postulates of. See C.F. Miller, III, On group-theoretic decision problems and their classification, Annals of Math. Studies 68 (). $\endgroup$ – John Stillwell May 25 '10 at 1. On Group-Theoretic Decision Problems and Their Classification.

(AM), Volume 68 () Vol. Shatz, Stephen S.: Profinite Groups, Arithmetic, and Geometry. (AM), Volume 67 () Vol. Ahlfors, Lars Valerian / Bers, Lipman: Advances in the Theory of.

Cool problems to impress students with group theory [closed] Ask Question Asked 10 (or 26 letters -- still even) for codes, Theorem 3 is annoying. The book community with their ISBN code got around this by using m = 11 with a special check digit of X (a few years ago they switched to m = 13).

Decision problems and group representations. This book is concerned with the mathematical, especially algebraic, aspects of cryptography.

It grew out of many courses presented by the authors over the past twenty years at various universities and covers a wide range of topics in mathematical cryptography. It is primarily geared towards graduate students and advanced undergraduates in. MSC Classification Codes. xx: General.

Instructional exposition (textbooks, tutorial papers, etc.) Research exposition (monographs, survey articles). In the mathematical subject of group theory, the Adian–Rabin theorem is a result which states that most "reasonable" properties of finitely presentable groups are algorithmically theorem is due to Sergei Adian () and, independently, Michael O.

Rabin (). Definition of group theoretic in the dictionary. Meaning of group theoretic. What does group theoretic mean. Information and translations of group theoretic in the most comprehensive dictionary definitions resource on the web.

For m> 4 group-theoretic decision problems prevent a complete classi ca-tion of m-dimensional manifolds, by the following argument. Every manifold M can be triangulated by a nite simplicial complex, so that the fundamental group ˇ1(M) is nitely presented.

Homotopy equivalent manifolds have isomorphic fun-damental groups.It is also worth noting that this could not be done using the essentially group-theoretic approaches of Clarke et al. First, a precise definition of "the" coarsest bisimulation in this context must be given; it would seem to inherently involve itself in some group-theoretic considerations relating to symmetries, considering that, for example.Geometric group theory is an area in mathematics devoted to the study of finitely generated groups via exploring the connections between algebraic properties of such groups and topological and geometric properties of spaces on which these groups act (that is, when the groups in question are realized as geometric symmetries or continuous transformations of some spaces).