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This is a Theoretical Analysis study.

September 10, 2025Comptes Rendus MathématiqueOpen Access

Groups acting on the line with at most 2 fixed points: an extension of Solodov’s theorem

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The result shows that groups acting on the line with up to two fixed points follow similar structures.
Non-trivial elements in these groups are shown to have at most two fixed points, supporting action types.
By extending Solodov's theorem, this work reveals insights on group actions in mathematical structures.
The definitions and classifications of these group actions are crucial for understanding their properties.

Implication

Theorem extends findings on group actions with up to two fixed points, indicating similar structures.

Abstract

A classical result by Solodov states that if a group acts on the line such that any non-trivial element has at most one fixed point, then the action is either abelian or semi-conjugate to an affine action. We show that the same holds if we relax the assumption, requiring that any non-trivial element has at most 2 fixed points.

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Cite This Study

João Carnevale (2025) studied this question.

synapsesocial.com/papers/68c1924e9b7b07f3a0616883 https://doi.org/10.5802/crmath.777

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Implication

Theorem extends findings on group actions with up to two fixed points, indicating similar structures.

Groups acting on the line with at most 2 fixed points: an extension of Solodov’s theorem

Key Points

Implication

Abstract

Discussion

Cite This Study

Groups acting on the line with at most 2 fixed points: an extension of Solodov’s theorem

Key Points

Implication

Abstract

Discussion

Cite This Study

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