Yong Yang
Published 2014-10-02Version 1
Let $G$ be a permutation group of degree $n$ and let $s(G)$ denote the number of set-orbits of $G$. We determine $\inf(\frac {\log_2 s(G)} n)$ over all groups $G$ that satisfy certain restrictions on composition factors (i.e. $Alt(k), k > 4$ cannot be obtained as a quotient of a subgroup of $G$).
The number of composition factors of order $p$ in completely reducible groups of characteristic $p$
On the orders of composition factors in completely reducible groups
On the Saxl graph of a permutation group
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