Geodesic
Restricted sumsets in finite nilpotent groups
Shanshan Du 1   ; Hao Pan 2
1 The Fundamental Division Jingling Institute of Technology Nanjing 211169 People’s Republic of China
2 Department of Mathematics Nanjing University Nanjing 210093 People’s Republic of China
Acta Arithmetica, Tome 178 (2017) no. 2, pp. 101-123 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Suppose that $A,B$ are non-empty subsets of the finite nilpotent group $G$. If $A\not=B$, then the cardinality of the restricted sumset $$A\mathbin\dotplus B=\{a+b:a\in A,\, b\in B,\, a\neq b\} $$ is at least $$\min\{p(G),|A|+|B|-2\},$$ where $p(G)$ denotes the least prime factor of $|G|$. Moreover we prove that if $A$ is a non-empty subset of a finite group $G$ with $|A| \lt (p(G)+3)/2$, then the elements of $A$ commute when $$ |A\mathbin\dotplus A|=2|A|-3. $$
DOI : 10.4064/aa7437-8-2016
Keywords: suppose non empty subsets finite nilpotent group nbsp cardinality restricted sumset mathbin dotplus neq least min where denotes least prime factor moreover prove non empty subset finite group elements commute mathbin dotplus

Shanshan Du  1   ; Hao Pan  2

1 The Fundamental Division Jingling Institute of Technology Nanjing 211169 People’s Republic of China
2 Department of Mathematics Nanjing University Nanjing 210093 People’s Republic of China 
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Shanshan Du; Hao Pan. Restricted sumsets in finite nilpotent groups. Acta Arithmetica, Tome 178 (2017) no. 2, pp. 101-123. doi: 10.4064/aa7437-8-2016

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