TY - JOUR ID - 108338 TI - A note on factorizations of finite groups JO - Journal of the Iranian Mathematical Society JA - JIMS LA - en SN - AU - Bergman, G. M. AD - Department of Mathematics, University of California Berkeley, CA 94720-3840 USA. Y1 - 2020 PY - 2020 VL - 1 IS - 2 SP - 157 EP - 161 KW - Factorization of a finite group KW - Product of subsets DO - 10.30504/jims.2020.108338 N2 - In Question 19.35 of the Kourovka Notebook, M. H. Hooshmand asks whether, given a finite group $G$ and a factorization $\mathrm{card}(G)= n_1\ldots n_k,$ one can always find subsets $A_1,\ldots,A_k$ of $G$ with $\mathrm{card}(A_i)=n_i$ such that $G=A_1\ldots A_k;$ equivalently, such that the group multiplication map $A_1\times\ldots\times A_k\to G$ is a bijection. We show that for $G$ the alternating goup on $4$ elements, $k=3,$ and $(n_1,n_2,n_3) = (2,3,2),$ the answer is negative. We then generalize some of the tools used in our proof, and note a related open question. UR - https://jims.ims.ir/article_108338.html L1 - https://jims.ims.ir/article_108338_8df75833b842c30981a08daf42636a75.pdf ER -