caa a22 4500 38637225X CHVBK 20180307112002.0 cr unu---uuuuu 161130e198905 xx s 000 0 eng 10.1017/S0017089500007795 doi S0017089500007795 pii (NATIONALLICENCE)cambridge-10.1017/S0017089500007795 The semigroup of one-to-one transformations with finite defects [Elektronische Daten] Let be the semigroup of all total one-to-one transformations of an infinite set X. For an ƒ let the defect of ƒ def ƒ, be the cardinality of X - R(ƒ), where R(ƒ) = ƒ(X) is the range of ƒ. Then is a disjoint union of the symmetric group x on X, the semigroup S of all transformations in with finite non-zero defects and the semigroup Ā of all transformations in S with infinite defects, such that S U Ā and Ā are ideals of . The properties of x and Ā have been investigated by a number of authors (for the latter it was done via Baer-Levi semigroups, see [2], [3], [5], [6], [7], [8], [9], [10] and note that Ā decomposes into a union of Baer-Levi semigroups). Our aim here is to study the semigroup S. It is not difficult to see that S is left cancellative (we compose functions ƒ, g in S as ƒg(x) = ƒ(g(x)), for x X) and idempotent-free. All automorphisms of S are inner [4], that is of the form ƒ → hƒhfh-1 ƒ S, h x. Copyright © Glasgow Mathematical Journal Trust 1989 Levi Inessa Department of Mathematics, University of Louisville, Lousville, Kentucky 40292 Schein Boris M. Department of Mathematical Sciences, University of Arkansas, Fayetteville, Arkansas 72701 Glasgow Mathematical Journal Cambridge University Press 31/2(1989-05), 243-249 0017-0895 31:2<243 1989 31 GMJ https://doi.org/10.1017/S0017089500007795 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0017089500007795 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Levi Inessa Department of Mathematics, University of Louisville, Lousville, Kentucky 40292 NATIONALLICENCE 700 1- Schein Boris M. Department of Mathematical Sciences, University of Arkansas, Fayetteville, Arkansas 72701 NATIONALLICENCE 773 0- Glasgow Mathematical Journal Cambridge University Press 31/2(1989-05), 243-249 0017-0895 31:2<243 1989 31 GMJ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge