Monogenic free inverse semigroups and partial automorphisms of regular rooted trees

Анотація

For a one-to-one partial mapping on an infinite set, we present a criterion in terms of its cycle-chain decomposition that the inverse subsemigroup generated by this mapping is monogenic free inverse.


We also give a sufficient condition for a regular rooted tree partial automorphism to extend to a partial automorphism of another regular rooted tree so that the inverse semigroup gene\-ra\-ted by this extended partial automorphism is monogenic free inverse. The extension procedure we develop is then applied to $n$-ary adding machines.

Біографії авторів

E. Kochubinska, Taras Shevchenko National University Kyiv Ukraine

Taras Shevchenko National University

Kyiv Ukraine

A. Oliynyk, Taras Shevchenko National University Kyiv Ukraine

Taras Shevchenko National University

Kyiv Ukraine

Посилання

K. Cvetko-Vah, D. Kokol Bukovˇsek, T. Koˇsir, G. Kudryavtseva, Y. Lavrenyuk, A. Oliynyk, Semitransitive subsemigroups of the symmetric inverse semigroups, Semigroup Forum, 78 (2009), №1, 138–147. https://doi.org/10.1007/s00233-008-9123-z

D. D’Angeli, E. Rodaro, J.P. W¨achter, On the structure theory of partial automaton semigroups, Semigroup Forum, 101 (2020), №1, 51–76. https://doi.org/10.1007/s00233-020-10114-5

O. Ganyushkin, V. Mazorchuk, Classical finite transformation semigroups, Springer-Verlag, 2009. https://doi.org/10.1007/978-1-84800-281-4

R. Grigorchuk, V. Nekrashevych, V. Sushchansky, Automata, dynamical systems, and groups, Tr. Mat. Inst. Steklova, 231 (2000), 134–214.

Y. Kochubinska, Combinatorics of partial wreath power of finite inverse symmetric semigroup ISd, Algebra Discrete Math., (2007), №1, 49–60.

E. Kochubinska, Spectral properties of partial automorphisms of a binary rooted tree, Algebra Discrete Math., 26 (2018), №2, 280–289.

E. Kochubinska, Spectrum of partial automorphisms of regular rooted tree, Semigroup Forum, 103 (2021), №2, 567–574. https://doi.org/10.1007/s00233-021-10219-5

J. Konieczny, Centralisers in the infinite symmetric inverse semigroup, Bull. Aust. Math. Soc., 87 (2013), №3, 462–479. https://doi.org/10.1017/S0004972712000779

S. Lipscomb, Symmetric inverse semigroups, American Mathematical Society, Providence, RI, 1996. https://doi.org/10.1090/surv/046

A. Oliynyk, On free semigroups of automaton transformations, Math. Notes, 63 (1998), №7, 215–2224. https://doi.org/10.1007/BF02308761

A. Oliynyk, V. Prokhorchuk, Amalgamated free product in terms of automata constructions, Comm. Algebra, 50 (2022), №2, 740–750. https://doi.org/10.1080/00927872.2021.196796

A. Oliynyk, V. Sushchansky, J. Slupik, Inverse semigroups of partial automaton permutations, Internat. J. Algebra Comput., 20 (2010), №7, 923–952. https://doi.org/10.1142/S0218196710005960

M. Petrich, Inverse semigroups, John Wiley & Sons, Inc., 1984.

J. Slupik, Classification of inverse semigroups generated by two-state partially defined invertible automata over the two-symbol alphabet, Algebra Discrete Math., (2006), №1, 67–80.

Опубліковано
2024-03-19
Як цитувати
Kochubinska, E., & Oliynyk, A. (2024). Monogenic free inverse semigroups and partial automorphisms of regular rooted trees. Математичні студії, 61(1), 3-9. https://doi.org/10.30970/ms.61.1.3-9
Розділ
Статті