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Infinite Group Theory: From the Past to the Future

Paul Baginski, Benjamin Fine, and Anthony M. Gaglione, editors
World Scientific
Publication Date: 
Number of Pages: 
[Reviewed by
Charles Traina
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Infinite Group Theory is a collection of thirteen papers presented at a conference held on April 23–24, 2015 in honor of the 70th birthdays of two group theorists, Gerhard Rosenberger and Dennis Spellman. The papers show the developments in group theory over several decades, especially in Combinatorial Group Theory.

The topics covered are: groups with the weak-minimal condition of non-permutable subgroups, secret sharing, orderable groups, topological groups, model theory, commutative transitivity and the CSA property, free Burnside groups, discrete subgroups of PSL(2,C), probabilistic reasoning under the principle of maximum entropy (MaxEnt Principle), infinite dimensional linear groups, Lie rings, conjugacy problem in wreath products, group presentations and Cayley graphs.

These toipcs show the impact of group theory and the use of Combinatorial Group Theory in different areas. They can serve as potential research topics and offer a convincing reason for the study of group theory.

Charles Traina is Professor of Mathematics at St. John’s University in New York.

  • Groups with the Weak Minimal Condition on Non-Permutable Subgroups (Laxmi K Chatuat and Martyn R Dixon)
  • A Survey: Shamir Threshold Scheme and Its Enhancements (Chi Sing Chum, Benjamin Fine, and Xiaowen Zhang)
  • The Zappa-Szep Product of Left-Orderable Groups (Fabienne Chouraqui)
  • Totally Disconnected Groups From Baumslag-Solitar Groups (Murray Elder and George Willis)
  • Elementary and Universal Theories of Nonabelian Commutative Transitive and CSA Groups (B Fine, A M Gaglione, and D Spellman)
  • Commutative Transitivity and the CSA Property (Benjamin Fine, Anthony Gaglione, Gerhard Rosenberger, and Dennis Spellman)
  • The Universal Theory of Free Burnside Groups of Large Prime Exponent (Anthony M Gaglione, Seymour Lipschutz, and Dennis Spellman)
  • Primitive Curve Lengths on Pairs of Pants (Jane Gilman)
  • Drawing Inferences Under Maximum Entropy From Relational Probabilistic Knowledge Using Group Theory (Gabriele Kern-Isberner, Marco Wilhelm, and Christoph Beierle)
  • On Some Infinite-Dimensional Linear Groups and the Structure of Related Modules (L A Kurdachenko and I Ya Subbotin)
  • On New Analogs of Some Classical Group Theoretical Results in Lie Rings (L A Kurdachenko, A A Pypka and I Ya Subbotin)
  • Log-Space Complexity of the Conjugacy Problem in Wreath Products (Alexei Myasnikov, Svetla Vassileva, and Armin Weiss)
  • Group Presentations, Cayley Graphs and Markov Processes (Peter Olszewski)