View source for Zassenhaus group

{{TEX|done}}{{MSC|20B20}}

A doubly-transitive group $G$ of permutations on a finite set $M$ (cf. [[Permutation group]]) in which only the identity permutation fixes more than two elements of $M$ and such that for any pair $a,b \in M$ the subgroup $H_{a,b}$ is non-trivial, where
$$
H_{a,b} = \{ h \in G : h(a)=a\,,\ h(b)=b \} \ ;
$$
such groups were first considered by H. Zassenhaus in [[#References|[1]]]. The class of Zassenhaus groups includes two families of finite simple groups: the projective [[special linear group]]s $\mathrm{PSL}(2,q)$, $q>3$, and the [[Suzuki group]]s.

====References====
<table>
<TR><TD valign="top">[1]</TD> <TD valign="top">  H. Zassenhaus,   "Kennzeichnung endlicher linearer Gruppen als Permutationsgruppen"  ''Abh. Math. Sem. Univ. Hamburg'' , '''11'''  (1935)  pp. 17–40</TD></TR>
<TR><TD valign="top">[2]</TD> <TD valign="top">  D. Gorenstein,   "Finite groups" , Harper &amp; Row  (1968)</TD></TR>
</table>



====Comments====


====References====
<table>
<TR><TD valign="top">[a1]</TD> <TD valign="top">  B. Huppert,   "Finite groups" , '''3''' , Springer  (1967)</TD></TR>
</table>