Locally maximal product-free sets of size 3

Hart, Sarah and Anabanti, Chimere (2015) Locally maximal product-free sets of size 3. Technical Report. Birkbeck College, University of London, London, UK.

Abstract

Let G be a group, and S a non-empty subset of G. Then S is product-free if ab =2 S for all a; b 2 S. We say S is locally maximal product-free if S is product-free and not properly contained in any other product-free set. A natural question is what is the smallest possible size of a locally maximal product-free set in G. The groups containing locally maximal product-free sets of sizes 1 and 2 were classi�ed in [3]. In this paper, we prove a conjecture of Giudici and Hart in [3] by showing that if S is a locally maximal product-free set of size 3 in a group G, then jGj � 24. This shows that the list of known locally maximal product-free sets given in [3] is complete.

Metadata

Statistics

Downloads

Export as XMLJSONCSV

Activity Overview

49Downloads

208Hits

Additional statistics are available via IRStats2.

Archive Staff Only (login required)

Edit/View Item