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Title page for ETD etd-11302012-113318


Type of Document Dissertation
Author Boatman, Nicholas Stephen
URN etd-11302012-113318
Title Partial-Burnside Groups
Degree PhD
Department Mathematics
Advisory Committee
Advisor Name Title
Alexander Olshanskiy Committee Chair
David Ernst Committee Member
Denis Osin Committee Member
Mark Sapir Committee Member
Michael Mihalik Committee Member
Keywords
  • small cancellation
  • geometric group theory
  • product variety
Date of Defense 2012-11-29
Availability unrestricted
Abstract
We consider groups which have a presentation whose defining relators are all nth powers and in which every element has order dividing n, for a fixed odd n that is sufficiently large. Such groups are called Partial-Burnside groups. We examine subgroups of such groups, showin that every noncyclic subgroup of a Partial-Burnside group contains a noncyclic Partial-Burnside group. We show that the word problem is solvable if and only if the conjugacy problem is solvable. Additionally, we show that every finitely presented subgroup contains a noncyclic free group. Finally, we show that various product varieties are not finitely based. In particular, in joint work with Olshanskii, we show that BpBp is not finitely based for large primes p, answering a question of Gupta and Krasilnikov.
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