Hart, Sarah and Anabanti, Chimere (2015) A note on filled groups. Technical Report. Birkbeck College, University of London, London, UK.
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Abstract
Let G be a finite group and S a subset of G. Then S is product-free if S \ SS = ;, and S fills G if G� � S [ SS. A product-free set is locally maximal if it is not contained in a strictly larger product-free set. Street and Whitehead [J. Combin. Theory Ser. A 17 (1974), 219–226] defined a group G as filled if every locally maximal product-free set in G fills G. Street and Whitehead classified all abelian filled groups, and conjectured that the finite dihedral group of order 2n is not filled when n = 6k +1 (k � 1). The conjecture was disproved by the current authors in [Austral. Journal of Combinatorics 63 (3) (2015), 385–398], where we also classified the filled groups of odd order. This brief note completes the classification of filled dihedral groups and discusses filled groups of order up to 100.
Metadata
| Item Type: | Monograph (Technical Report) |
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| Additional Information: | Birkbeck Pure Mathematics Preprint Series #17 |
| School: | Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences |
| Depositing User: | Sarah Hart |
| Date Deposited: | 12 Oct 2016 12:41 |
| Last Modified: | 09 Aug 2023 12:38 |
| URI: | https://eprints.bbk.ac.uk/id/eprint/16182 |
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