Abstract:
Suppose G is a transitive permutation group operating on a finite set $Omega$ and let p be a prime divisor of |G|. The smallest number of points moved by a non-identity p-Element is called the minimal p-degree of G and is denoted $m_p(G)$.
In this work the minimal p-degrees of various primitive permutation groups are determined. In addition, using the classification of the finite simple groups, it is shown, that with one classified exception - $m_p(G) geq frac{p-1}{p+1} cdot |Omega|$ holds, if G is primitive.
Furthermore conditions on primitive permutation groups G and prime divisors p
of |G| are derived, which ensure that $m_p(G) < frac{p-1}{p} cdot |Omega|$ holds. In particular the thesis comprises the classification of all primitive actions of Lie-groups G $in$ L(q) and all prime divisors p coprime to q with $m_p(G) < frac{p-1}{p} cdot |Omega|$.