1994/01/28 by Charles C. Sims · 5 citations
Computer Science · Biochemistry, Genetics and Molecular Biology · Mathematics · #semigroups and automata theory #DNA and Biological Computing #Cellular Automata and Applications #Coset #Rewriting #Quotient #Abelian group #Automaton #Computation #Mathematics #Algebra over a field #Group (periodic table) #Discrete mathematics #Pure mathematics #Computer science #Theoretical computer science #Programming language #Algorithm #Physics
paper · doi:10.1017/cbo9780511574702
openalex publication_date 1994/01/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/21
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.