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Results tagged with gr.group-theory
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user 527577
Questions about the branch of algebra that deals with groups.
2
votes
1
answer
132
views
Are the Baumslag–Solitar groups locally indicable groups?
BS(1,-1) is a right-ordered and locally indicable group. Additionally, BS(1,n) where n is a positive integer are ordered groups, therefore they are also locally indicable groups. What can be said abou …
2
votes
1
answer
381
views
Suppose $G$ is Conradian right-ordered group. If $x < z$ and $y < z$, can we say $xy < z^2$?
Suppose $G$ is Conradian right-ordered group. If $x < z$ and $y < z$, can we say $xy < z^2$?
In right-ordered groups, there is a result in Conrad - Right-ordered groups that states: If a group is a Co …
1
vote
0
answers
37
views
Lower bound for restricted sumset in ordered groups
Recently in The restricted sumsets in finite abelian groups it is proved that
Suppose that $k \geq 2$ and $A$ is a non-empty subset of a finite abelian
group $G$ with $|G| > 1$. Then the cardinality …
5
votes
0
answers
536
views
A problem on additive combinatorics in right-ordered groups
In a paper Small doubling in ordered groups: generators and structure it is proven in Lemma 4 page no. 598 that:
Let $G$ be an ordered group. Let $S$ be a finite subset of $G$ with at least two eleme …
7
votes
1
answer
498
views
Are Artin-Tits groups ordered groups?
We consider Artin-Tits groups of two generators $(I_2(n))$. Are these groups ordered groups?