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21.115 (2026)

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Let $C_1, \dots, C_n$ be (left or right) cosets of a finite group $G$ such that $U := C_1 \cup \dots \cup C_n$ is not $G$. Is it always true that $|G \setminus U| \geqslant |G|/2^n$?

Contributor: B. Sambale

Progress

Affirmative answers are known in some special cases (B. Sambale, M. Tărnăuceanu, J. Algebraic Combin., 55 (2022), 979–987).

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