University of Illinois Urbana-Champaign

Decision Problems in Restricted Classes of Groups

Lockhart, Jody Meyer

This item is only available for download by members of the University of Illinois community. Students, faculty, and staff at the U of I may log in with your NetID and password to view the item. If you are trying to access an Illinois-restricted dissertation or thesis, you can request a copy through your library's Inter-Library Loan office or purchase a copy directly from ProQuest.

Permalink

https://hdl.handle.net/2142/68177

Description

Title
Decision Problems in Restricted Classes of Groups
Author(s)
Lockhart, Jody Meyer
Issue Date
1980
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
Abstract
  • It is known that many decision problems are unsolvable in the class of all finitely presented groups. When the class of groups is restricted, problems previously unsolvable can become solvable. In this work we investigate decision problems for various restricted classes of groups.
  • We first consider the classes of finitely presented groups for which each group has solvable (lamda)-problem, where (lamda) is conjugacy, order and power. We show that "Markov-type" problems are unsolvable in these classes. We next consider recursively enumerable classes of group presentations (both finite presentations and infinite presentations) that have uniformly solvable word problem. We show that for classes of recursively generated, recursively related presentations of this type most problems are unsolvable. For classes of finite presentations with uniformly solvable word problem, the properties "having solvable order problem", "having solvable power problem", and "being torsion free" are recursively unrecognizable. Finally, we investigate the triviality problem for classes of finite presentations of groups and semigroups with deficiency close to zero. We show that the class of semigroup presentations of deficiency -1 and the class of group presentations of deficiency -11 have unsolvable triviality problem.
Graduation Semester
1980
Type of Resource
text
Permalink
http://hdl.handle.net/2142/68177

Owning Collections

Graduate Dissertations and Theses at Illinois PRIMARY
Graduate Theses and Dissertations at Illinois
Dissertations and Theses - Mathematics