A Zassenhaus group is a permutation group G on a finite set X with the following three properties:
- G is doubly transitive.
- Non-trivial elements of G fix at most two points.
- G has no regular normal subgroup. ("Regular" means that non-trivial elements do not fix any points of X; compare free action.)
The degree of a Zassenhaus group is the number of elements of X.
Some authors omit the third condition that G has no regular normal subgroup. This condition is put in to eliminate some "degenerate" cases. The extra examples one gets by omitting it are either Frobenius groups or certain groups of degree 2p and order 2p(2p − 1)p for a prime p, that are generated by all semilinear mappings and Galois automorphisms of a field of order 2p.
Read more about Zassenhaus Group: Examples, Further Reading
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