Finite Permutation Groups

By P. Müller. 2013

490 citations recorded by the source corpus.

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Between primitive and 2-transitive: Synchronization and its friends (2015, background): “For general references on permutation groups, we recommend [35, 47, 113].”
On the trigonometric moment problem (2011, unknown): “, n+m} is called a block ([22]) of GP ⊆ Sn+m if for each σ ∈ GP , either σ(B) = B or σ(B) ∩B = ∅.”
Finite Simple Groups (2016, background): “A classical result of Jordan asserts that there are no sharply t-transitive subgroups of Sym(n) for 6 6 t < n− 2; moreover the group M12 is the only finite permutation group which is sharply 5-transitive on a set of size n > 7 (see, for instance [37]).”
Supercharacter Theory Constructions Corresponding to Schur Ring Products (2012, background): “Note that the partition is completely determined by the ring A. S-rings were originally used by Schur and Wielandt in the study of permutation groups [19, pp. 403–412], but recently they have found applications in algebraic combinatorics, especially in the study of Cayley graphs.”