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Groups with Solvable Word Problems (Classic Reprint) (9780331786002)



Excerpt from Groups With Solvable Word Problems Equating truth in G with derivability from a set of axioms suggests the possibility of formulating the word problem for G as the derivability problem for some type of formal system. The first part of the paper is concerned with this. Once this is done, we can consider the questions usually asked about formal systems, such as consistency, decid ability, and completeness, and use results about particular formal systems to obtain results about groups and semigroups corresponding to these systems. In this analogy, nontrivial groups correspond to consistent systems, groups with solvable word problem to decidable systems, and simple groups to complete systems. The last analogy is particularly striking, for, strangely enough, although it has been known for a long time that complete recursively axiomatized theories are decidable, it was only recently noted that recursively presented simple groups have solvable word problems. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.


Product details

  • Hardback | 88 pages
  • 152 x 229 x 6mm | 277g
  • English
  • 40 Illustrations; Illustrations, black and white
  • 0331786001
  • 9780331786002


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