Multiple transitivity except for a system of imprimitivity

Title: Multiple transitivity except for a system of imprimitivity
Creator: Reid, Colin D.
Relation: ARC.FL170100032 http://purl.org/au-research/grants/arc/FL170100032
Relation: Journal of Group Theory Vol. 27, Issue 4, p. 651-712
Publisher Link: http://dx.doi.org/10.1515/jgth-2023-0062
Publisher: De Gruyter
Resource Type: journal article
Date: 2024
Description: Let Ω be a set equipped with an equivalence relation ∼ ; we refer to the equivalence classes as blocks of Ω. A permutation group G≤Sym(Ω) is 𝑘-by-block-transitive if ∼ is 𝐺-invariant, with at least 𝑘 blocks, and 𝐺 is transitive on the set of 𝑘-tuples of points such that no two entries lie in the same block. The action is block-faithful if the action on the set of blocks is faithful. In this article, we classify the finite block-faithful 2-by-block-transitive actions. We also show that, for k≥3 , there are no finite block-faithful 𝑘-by-block-transitive actions with nontrivial blocks.
Subject: transitivity; imprimitivity; block-faithful; k-by-block-transitive
Identifier: http://hdl.handle.net/1959.13/1511825
Identifier: uon:56554
Identifier: ISSN:1433-5883
Language: eng
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