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2 results

  • GROWTHS OF ENDOMORPHISMS OF FINITELY GENERATED SEMIGROUPS

  • Part of
  • ALAN J. CAIN, VICTOR MALTCEV
  • Journal:
    Journal of the Australian Mathematical Society / Volume 102 / Issue 2 / April 2017
    Published online by Cambridge University Press:
    08 July 2016, pp. 163-184
    Print publication:
    April 2017
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  • This paper studies the growths of endomorphisms of finitely generated semigroups. The growth is a certain dynamical characteristic describing how iterations of the endomorphism ‘stretch’ balls in the Cayley graph of the semigroup. We make a detailed study of the relation of the growth of an endomorphism of a finitely generated semigroup and the growth of the restrictions of the endomorphism to finitely generated invariant subsemigroups. We also study the possible values endomorphism growths can attain. We show the role of linear algebra in calculating the growths of endomorphisms of homogeneous semigroups. Proofs are a mixture of syntactic algebraic rewriting techniques and analytical tricks. We state various problems and suggestions for future research.

  • On representations of variants of semigroups

  • Ganna Kudryavtseva, Victor Maltcev
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 73 / Issue 2 / April 2006
    Published online by Cambridge University Press:
    17 April 2009, pp. 273-283
    Print publication:
    April 2006
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  • We construct a family of representations of an arbitrary variant Sa of a semigroup S, induced by a given representation of S, and investigate properties of such representations and their kernels.