The proportion of derangements characterizes the symmetric and alternating groups
Let $G$ be a subgroup of the symmetric group $S_n$. If the proportion of fixed-point-free elements in $G$ (or a coset) equals the proportion of fixed-point-free elements in $S_n$, then $G=S_n$. The analogue for $A_n$ holds if $n \ge 7$. We give an application to monodromy groups.
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2022
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| Online Access: | https://hdl.handle.net/1721.1/145830 |