Highly transitive actions of free products
Soyoung Moon, Yves Stalder
TL;DR
This paper characterizes free products that can act faithfully and highly transitively on countable sets, highlighting that groups like PSL(2,Z) have such actions, expanding understanding of their symmetry properties.
Contribution
It provides a characterization of free products with faithful, highly transitive actions and demonstrates that PSL(2,Z) admits such an action.
Findings
PSL(2,Z) admits a faithful, highly transitive action
Characterization of free products with highly transitive actions
Extension of symmetry understanding in free product groups
Abstract
We characterize free products admitting a faithful and highly transitive action. In particular, we show that the group admits a faithful and highly transitive action on a countable set.
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