ON THE HEIGHT AND RELATIONAL COMPLEXITY OF A FINITE PERMUTATION GROUP

Abstract Let G be a permutation group on set $\Omega $ of size t . We say that $\Lambda \subseteq \Omega is an independent if its pointwise stabilizer not equal to the any proper subset define height maximum set, and we denote this quantity $\textrm{H}(G)$ In paper, study for case when primitive. Our main result asserts either $\textrm{H}(G)< 9\log t$ or else in particular well-studied family (the primitive large–base groups ). An immediate corollary characterization with large relational complexity , latter being statistic introduced by Cherlin his model theory groups. also $\textrm{I}(G)$ length irredundant base which prove primitive, then $\textrm{I}(G)<7\log else, again, (which includes as well some others).