Essential Dimensions of A_7 and S_7
Alexander Duncan
TL;DR
This paper establishes that over any field of characteristic zero, the essential dimensions of the groups A_7 and S_7 are both equal to 4, using results related to finite subgroups of the Cremona group.
Contribution
It proves the exact essential dimensions of A_7 and S_7 are 4, extending previous knowledge through application of Prokhorov's results on finite subgroups.
Findings
Essential dimensions of A_7 and S_7 are both 4
Results hold over any field of characteristic zero
Utilizes Prokhorov's work on finite subgroups of the Cremona group
Abstract
We show that Y. Prokhorov's "Simple Finite Subgroups of the Cremona Group of Rank 3" implies that, over any field of characteristic 0, the essential dimensions of the alternating group, A_7, and the symmetric group, S_7, are 4.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Finite Group Theory Research