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Two generalizations of homogeneity in groups with applications to regular semigroups
2015
Transactions of the American Mathematical Society
Let X be a finite set such that |X| = n and let i j n. A group G S n is said to be (i, j)-homogeneous if for every I, J ⊆ X, such that |I| = i and |J| = j, there exists g ∈ G such that Ig ⊆ J. (Clearly (i, i)-homogeneity is i-homogeneity in the usual sense.) A group G S n is said to have the k-universal transversal property if given any set I ⊆ X (with |I| = k) and any partition P of X into k blocks, there exists g ∈ G such that Ig is a section for P . (That is, the orbit of each k-subset of X
doi:10.1090/tran/6368
fatcat:wnqtsvmmgrbrnceybfc53t33wa