Regular orbits of symmetric and alternating groups

Joanna B. Fawcett; E. A. O'Brien; Jan Saxl

doi:10.1016/j.jalgebra.2016.02.018

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arXiv · 1812.05880

Regular orbits of symmetric and alternating groups

Joanna B. Fawcett·E. A. O'Brien·Jan Saxl

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Abstract

Given a finite group $G$ and a faithful irreducible $FG$-module $V$ where $F$ has prime order, does $G$ have a regular orbit on $V$? This problem is equivalent to determining which primitive permutation groups of affine type have a base of size 2. In this paper, we classify the pairs $(G,V)$ for which $G$ has a regular orbit on $V$ where $G$ is a covering group of a symmetric or alternating group and $V$ is a faithful irreducible $FG$-module such that the order of $F$ is prime and divides the order of $G$.

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BibTeX RIS

Joanna B. Fawcett, E. A. O'Brien, Jan Saxl. 2018-12-14. Regular orbits of symmetric and alternating groups. https://doi.org/10.1016/j.jalgebra.2016.02.018

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