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- W2950614234 abstract "Let $ A$ be a subset of group $G_0$ with $|{A^{-1}A}|le 2|A|-2.$ We show that there are an element $ain A$ and a non-null proper subgroup $H$ of $G$ such that one of the following holds: begin{itemize} item $x^{-1}Hy subset A^{-1}A,$ for all $(x,y)in A^2setminus (Ha)^2,$ item $xHy^{-1} subset AA^{-1},$ for all $(x,y)in A^2setminus (aH)^2.$ end{itemize} where $G$ is the subgroup generated by ${A^{-1}A}.$ Assuming that $A^{-1}Aneq G$ and that $ |A^{-1}A|< frac{5|A|}3,$ we show that there are a normal subgroup $K$ of $G$ and a subgroup $H$ with $Ksubset Hsubset A^{-1}A $ and $2|K|ge |H|$ such that $$A^{-1}AK=KA^{-1}A=A^{-1}A text{and} 6|K|ge |A^{-1}A|=3|H|.$$" @default.
- W2950614234 created "2019-06-27" @default.
- W2950614234 creator A5002231659 @default.
- W2950614234 date "2010-06-25" @default.
- W2950614234 modified "2023-09-25" @default.
- W2950614234 title "Two Inverse results" @default.
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