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The automorphism group of the semigroup of finite complexes of a periodic abelian group

Published online by Cambridge University Press:  09 April 2009

R. D. Byrd ,
J. T. Lloyd  and
J. W. Stepp
R. D. Byrd
Affiliation:
Department of Mathematics, University of Houston, Houston, Texas 77004, USA.
J. T. Lloyd
Affiliation:
Department of Mathematics, University of Houston, Houston, Texas 77004, USA.
J. W. Stepp
Affiliation:
Department of Mathematics, University of Houston, Houston, Texas 77004, USA.
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Abstract

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In this paper it is shown that if G is a periodic Abelian group and ∣ G ∣ ≥ 6, then the only automorphisms of the semigroup of finite nonempty complexes of G are induced by automorphisms of G.

Subject classification (Amer. Math. Soc. (MOS) 1970): primary 20 M 15; secondary 20 K 30.

Keywords

automorphismperiodic Abelian groupsemigroup
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 28 , Issue 1 , August 1979 , pp. 15 - 22
Copyright
Copyright © Australian Mathematical Society 1979

References

Byrd, R. D., Lloyd, J. T., Mena, R. A. and Teller, J. R. (1977), “Retractable groups”, Acta Math. Acad. Sci. Hungar. 29, 219–233.CrossRefGoogle Scholar
Byrd, R. D., Lloyd, J. T., Pedersen, F. D. and Stepp, J. W. (1977), “Automorphisms of the semigroup of finite complexes of a periodic locally cyclic group”, Pacific J. Math. 72, 27–39. (BLPSa)Google Scholar
Byrd, R. D., Lloyd, J. T., Pederson, F. D. and Stepp, J. W. (1978), “Automorphisms of the semigroup of finite complexes of a locally finite group”, J. Reine Angew. Math. 299/300, 151–160. (BLPSb)Google Scholar
Byrd, R. D., Lloyd, J. T., Pederson, F. D. and Stepp, J. W. (1979), “Automorphisms of the semigroup of finite complexes of a torsion-free abelian group” (submitted). (BLPSc)Google Scholar
Lau, A. (1979), “Finite abelian semigroups represented into the power set of finite groups” (submitted).Google Scholar
Mann, H. B. (1952), “On products of sets of group elements”, Canad. J. Math. 4, 64–66.Google Scholar
Mann, H. B. (1953), “An addition theorem for sets of elements of an abelian group”, Proc. Amer. Math. Soc. 4, 423.Google Scholar
Trnkova, V. (1975), “On a representation of commutative semigroups, Semigroup Forum 10, 203–214.CrossRefGoogle Scholar