Groups containing small locally maximal productfree sets
Hart, Sarah and Anabanti, Chimere (2016) Groups containing small locally maximal productfree sets. International Journal of Combinatorics , p. 8939182. ISSN 16879163.

Text
LMPFSsize3.pdf  Author's Accepted Manuscript Download (245kB)  Preview 
Abstract
Let G be a group, and S a nonempty subset of G. Then S is productfree if ab is not in S for all a, b in S. We say S is locally maximal productfree if S is productfree and not properly contained in any other productfree set. A natural question is to determine the smallest possible size of a locally maximal productfree set in G. Alternatively, given a positive integer k, one can ask: what is the largest integer n_k such that there is a group of order n_k with a locally maximal productfree set of size k? The groups containing locally maximal productfree sets of sizes 1 and 2 are known, and it has been conjectured that n_3 = 24. The purpose of this paper is to prove this conjecture and hence show that the list of known locally maximal productfree sets of size 3 is complete. We also report some experimental observations about the sequence n_k.
Metadata
Item Type:  Article 

School:  Birkbeck Schools and Departments > School of Business, Economics & Informatics > Economics, Mathematics and Statistics 
Depositing User:  Sarah Hart 
Date Deposited:  07 Oct 2016 14:54 
Last Modified:  20 Jan 2017 10:49 
URI:  http://eprints.bbk.ac.uk/id/eprint/16146 
Statistics
Additional statistics are available via IRStats2.