Permutation Groups and Orbits on Power Sets

Yong Yang

Permutation Groups and Orbits on Power Sets

Group Theory 2014-10-03 v1

Authors: Yong Yang

Abstract

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 $G$ ).

Keywords

permutation groups permutations finite group theory

Cite

@article{arxiv.1410.0420,
  title  = {Permutation Groups and Orbits on Power Sets},
  author = {Yong Yang},
  journal= {arXiv preprint arXiv:1410.0420},
  year   = {2014}
}

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