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- W2963895772 abstract "The classification of flag-transitive generalized quadrangles is a long-standing open problem at the interface of finite geometry and permutation group theory. Given that all known flag-transitive generalized quadrangles are also point-primitive (up to point–line duality), it is likewise natural to seek a classification of the point-primitive examples. Working toward this aim, we are led to investigate generalized quadrangles that admit a collineation group $G$ preserving a Cartesian product decomposition of the set of points. It is shown that, under a generic assumption on $G$ , the number of factors of such a Cartesian product can be at most four. This result is then used to treat various types of primitive and quasiprimitive point actions. In particular, it is shown that $G$ cannot have holomorph compound O’Nan–Scott type. Our arguments also pose purely group-theoretic questions about conjugacy classes in nonabelian finite simple groups and fixities of primitive permutation groups." @default.
- W2963895772 created "2019-07-30" @default.
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- W2963895772 date "2017-09-14" @default.
- W2963895772 modified "2023-10-11" @default.
- W2963895772 title "SIMPLE GROUPS, PRODUCT ACTIONS, AND GENERALIZED QUADRANGLES" @default.
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- W2963895772 doi "https://doi.org/10.1017/nmj.2017.35" @default.
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