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Tagged with sumset abelian-groups
3
questions
4
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1
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183
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Two uncountable subsets of real numbers without any interval and two relations
Are there two uncountable subsets $A, B$ of real numbers such that:
(1) $(A-A)\cap (B-B)=\{ 0\}$,
(2) $(A-A)+B=\mathbb{R}$ or $(B-B)+A=\mathbb{R}$ ?
We know that if one of them contains an interval,...
- 2,491
1
vote
0
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88
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Coset Progression is Freiman Isomorphic to Bohr Set
For an abelian group $G$, $H$ a finite subgroup of $G$, $x_1, \dots, x_r \in G$ and $L_1, \dots, L_r \in \mathbb N$, let:
$P(x ; L) = P(x_1, \dots, x_r ; L_1, \dots, L_r) = \{l_1x_1 + \dots + l_rx_r ...
- 2,683
2
votes
1
answer
67
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Prove that if $|A+A| \leq K|A|$ then $2A - 2A$ is a $K^{16}$-approximate group.
Let $A$ be a finite subset of an abelian group, $G$ (call the operation addition). We say $A$ is a $K$-approximate group if:
1) $e_G \in A$
2) $A^{-1} = \{ a^{-1} \mid a \in A \} = A$
3) $\exists X ...
- 2,683