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Fixed-Point-Free Permutation Properties in Groups and Semigroups

机译：群和半群中的无定点置换性质

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摘要

We say that a semigroup S is (fixed-point-free, for short f.p.f.) permutable, if,for some integer n and for every x(sub 1),...,x(sub n) in S, there exists a non-trivial (fixed-point-free) permutation sigma on (1,...,n), such that: x(sub 1),...,x(sub n) = x(sub sigma(1)),...,x(sub sigma(n)). In this paper we present the results of a systematical study of fixed-point-free permutation, pointing out the main differences from the well-known permutation property for semigroups and groups. To supply an interesting example, we study into details the f.p.f. permutation property in dihedral groups.

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