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arXiv · 2012.07415

A subexponential bound on the cardinality of abelian quotients in finite transitive groups

Andrea Lucchini·Luca Sabatini·Pablo Spiga
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Abstract

We show that, for every transitive group $G$ of degree $n\ge 2$, the largest abelian quotient of $G$ has cardinality at most $4^{n/\sqrt{\log_2 n}}$. This gives a positive answer to a 1989 outstanding question of L\'aszl\'o Kov\'acs and Cheryl Praeger.

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Andrea Lucchini, Luca Sabatini, Pablo Spiga. 2020-12-14. A subexponential bound on the cardinality of abelian quotients in finite transitive groups. https://doi.org/10.1112/blms.12532

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