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Zassenhaus group

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A doubly-transitive group of permutations on a finite set (cf. Permutation group) in which only the identity permutation fixes more than two elements of and such that for any pair the subgroup is non-trivial, where

such groups were first considered by H. Zassenhaus in [1]. The class of Zassenhaus groups includes two families of finite simple groups: the projective special linear groups , (cf. Special linear group), and the Suzuki groups (cf. Suzuki group).

References

[1] H. Zassenhaus, "Kennzeichnung endlicher linearer Gruppen als Permutationsgruppen" Abh. Math. Sem. Univ. Hamburg , 11 (1935) pp. 17–40
[2] D. Gorenstein, "Finite groups" , Harper & Row (1968)


Comments

References

[a1] B. Huppert, "Finite groups" , 3 , Springer (1967)
How to Cite This Entry:
Zassenhaus group. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Zassenhaus_group&oldid=12647
This article was adapted from an original article by N.N. Vil'yams (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article