Groups containing locally maximal product-free sets of size 4

• Published in: Algebra and Discrete Mathematics
• Date: 2021
• Main Author: Anabanti, C.S.
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2021
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/188705
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Groups containing locally maximal product-free sets of size 4 / C.S. Anabanti // Algebra and Discrete Mathematics. — 2021. — Vol. 31, № 2. — С. 167–194. — Бібліогр.: 12 назв. — англ.

Every locally maximal product-free set S in a finite group G satisfies G = S ∪ SS ∪ S⁻¹S ∪ SS⁻¹ ∪ √S, where SS = {xy | x, y ∈ S}, S⁻¹S = {x⁻¹y | x, y ∈ S}, SS⁻¹ = {xy⁻¹ | x, y ∈ S} and √S = {x ∈ G | x² ∈ S}. To better understand locally maximal product-free sets, Bertram asked whether every locally...