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Results tagged with gr.group-theory
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user 119181
Questions about the branch of algebra that deals with groups.
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Ordered group acting freely on partially ordered set
Let $(G, <)$ be a totally ordered group, and let $<$ be left-invariant. Let $G$ act (freely?) on a partially ordered set $(S, <)$, such that this group action preserves the ordering:
$$ s_1 < s_2 …
CommunityBot
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Relations between $\Omega$-groups, locally indicable groups, and right-orderable groups
We know that the class of right-orderable groups $\mathit{RO}$, is contained in the class of $\Omega$-groups (read it from "A note on group rings of certain torsion-free groups" by Burns-Hale).
A gro …
- 63.9k
-1
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Groups With Arbitrarily Large Torsion [closed]
Thompson's Group has two well known presentations:
$\langle x_0,x_1, ... $ | $ x_k^{-1} x_n x_k = x_{n+1}\forall k < n \rangle$
$\langle A,B $ | $ [AB^{-1}, A^{-1}BA], [AB^{-1}, A^{-2}BA^2] \rangle$ …
- 8,401
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A Backtrack as a Single Word in a Group Presentation yields a Complex that isn't of the Same...
By "backtrack" I mean a subword of a relator in a group presentation of the form $x x^{-1}$.
Let $X = \langle a \rangle$ as a presentation complex.
Let $Y = \langle a$ | $aa^{-1} \rangle$ as a pre …
- 25k