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On the relational complexity of a finite permutation group. (English) Zbl 1378.20001

The relational complexity \(\rho\) of a permutation group was introduced by the author et al. [J. Comb. Theory, Ser. A 74, No. 2, 249–286 (1996; Zbl 0854.20002)]. The author determines all finite primitive affine permutation groups with relational complexity \(\phi =2\); the proof requires the classification of the finite simple groups. Moreover, he corrects the computation of \(\rho\) for alternating groups acting on \(k\)-sets, correcting a statement in [the author, in: The Gelfand Mathematical Seminars, 1996–1999. Dedicated to the memory of Chih-Han Sah. Boston, MA: Birkhäuser. 15–48 (2000; Zbl 0955.03040)].

MSC:

20B05 General theory for finite permutation groups
20B15 Primitive groups
20B10 Characterization theorems for permutation groups
20B25 Finite automorphism groups of algebraic, geometric, or combinatorial structures
03C13 Model theory of finite structures
03C60 Model-theoretic algebra
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References:

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