### Abstract

We report on what we call the Hamidoune problem, inspired by a problem by Dicks and Ivanov. The problem asks if the inequality |A|+|B|-12|AB|-12|A{dot operator}2B|≤max{2,|gH|:H≤G,g∈G,gH⊆A{dot operator}2B} holds when A and B are finite subsets of a group G, each one with at least two elements, and A{dot operator}2B denotes the set of elements which can be written in at least two different ways as a product of one element in A and one in B. © 2013 Elsevier Ltd.

Original language | English |
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Pages (from-to) | 1326-1330 |

Journal | European Journal of Combinatorics |

Volume | 34 |

Issue number | 8 |

DOIs | |

Publication status | Published - 1 Nov 2013 |

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## Cite this

Dicks, W., & Serra, O. (2013). The Dicks-Ivanov problem and the Hamidoune problem.

*European Journal of Combinatorics*,*34*(8), 1326-1330. https://doi.org/10.1016/j.ejc.2013.05.015