
TL;DR
This paper constructs the first examples of sharply 3-transitive groups that do not originate from near fields, showing a new class of such groups with unique stabilizer properties.
Contribution
It introduces the first sharply 3-transitive groups not derived from near fields, expanding the understanding of permutation group structures.
Findings
Constructed new sharply 3-transitive groups without near field origin
Point stabilizers lack nontrivial abelian normal subgroups
Demonstrated existence of groups with novel transitivity properties
Abstract
We construct the first sharply -transitive groups not arising from a near field, i.e. point stabilizers have no nontrivial abelian normal subgroup.
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