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Computation with Finitely Presented Groups

1994-01-28 Mathematics
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Release : 1994-01-28
Genre : Mathematics
Kind : eBook
Book Rating : 138/5 ( reviews)

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Book Synopsis Computation with Finitely Presented Groups by : Charles C. Sims

Download or read book Computation with Finitely Presented Groups written by Charles C. Sims. This book was released on 1994-01-28. Available in PDF, EPUB and Kindle. Book excerpt: Research in computational group theory, an active subfield of computational algebra, has emphasised three areas: finite permutation groups, finite solvable groups, and finitely presented groups. This book deals with the third of these areas. The author emphasises the connections with fundamental algorithms from theoretical computer science, particularly the theory of automata and formal languages, computational number theory, and computational commutative algebra. The LLL lattice reduction algorithm and various algorithms for Hermite and Smith normal forms from computational number theory are used to study the abelian quotients of a finitely presented group. The work of Baumslag, Cannonito and Miller on computing nonabelian polycyclic quotients is described as a generalisation of Buchberger's Gröbner basis methods to right ideals in the integral group ring of a polycyclic group. Researchers in computational group theory, mathematicians interested in finitely presented groups and theoretical computer scientists will find this book useful.

Finitely Presented Groups

2024-10-07 Mathematics
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Release : 2024-10-07
Genre : Mathematics
Kind : eBook
Book Rating : 570/5 ( reviews)

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Book Synopsis Finitely Presented Groups by : Volker Diekert

Download or read book Finitely Presented Groups written by Volker Diekert. This book was released on 2024-10-07. Available in PDF, EPUB and Kindle. Book excerpt: This book contains surveys and research articles on the state-of-the-art in finitely presented groups for researchers and graduate students. Overviews of current trends in exponential groups and of the classification of finite triangle groups and finite generalized tetrahedron groups are complemented by new results on a conjecture of Rosenberger and an approximation theorem. A special emphasis is on algorithmic techniques and their complexity, both for finitely generated groups and for finite Z-algebras, including explicit computer calculations highlighting important classical methods. A further chapter surveys connections to mathematical logic, in particular to universal theories of various classes of groups, and contains new results on countable elementary free groups. Applications to cryptography include overviews of techniques based on representations of p-groups and of non-commutative group actions. Further applications of finitely generated groups to topology and artificial intelligence complete the volume. All in all, leading experts provide up-to-date overviews and current trends in combinatorial group theory and its connections to cryptography and other areas.

Handbook of Computational Group Theory

2005-01-13 Mathematics
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Release : 2005-01-13
Genre : Mathematics
Kind : eBook
Book Rating : 215/5 ( reviews)

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Book Synopsis Handbook of Computational Group Theory by : Derek F. Holt

Download or read book Handbook of Computational Group Theory written by Derek F. Holt. This book was released on 2005-01-13. Available in PDF, EPUB and Kindle. Book excerpt: The origins of computation group theory (CGT) date back to the late 19th and early 20th centuries. Since then, the field has flourished, particularly during the past 30 to 40 years, and today it remains a lively and active branch of mathematics. The Handbook of Computational Group Theory offers the first complete treatment of all the fundame

Methods for Investigating Finitely-presented Groups

2011 Computer algorithms
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Release : 2011
Genre : Computer algorithms
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Book Synopsis Methods for Investigating Finitely-presented Groups by : Matthew Auger

Download or read book Methods for Investigating Finitely-presented Groups written by Matthew Auger. This book was released on 2011. Available in PDF, EPUB and Kindle. Book excerpt: This thesis concerns computation with finite group presentations and its application to resolve certain open problems of Kim and Kostrikin. We use the low-index subgroups and abelian quotient invariants algorithms to show that each member of a certain family of finitely-pesented groups is infinite. We present a new algorithm for determining which generalised dihedral groups are quotients of a given finitely-presented group, and use this to show that the groups in another family are pairwise non-isomorphic. Also we describe the method of 'pictures' over group presentations, discussing what they represent and how they can be used to obtain information about the group.

Computation with Finitely L-presented Groups

2012
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Release : 2012
Genre :
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Book Synopsis Computation with Finitely L-presented Groups by : René Hartung

Download or read book Computation with Finitely L-presented Groups written by René Hartung. This book was released on 2012. Available in PDF, EPUB and Kindle. Book excerpt:

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