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@article{1733940,
author = {Kaďourek, Jiří},
article_number = {4},
doi = {http://dx.doi.org/10.1017/S0013091520000218},
keywords = {pseudovarieties of finite monoids; pseudovarieties of finite groups; semidirect products of monoids; semidirectly closed pseudovarieties; finite inverse monoids; finite aperiodic monoids; finite R-trivial monoids; finite p-groups; solvable groups},
language = {eng},
issn = {0013-0915},
journal = {Proceedings of the Edinburgh Mathematical Society},
title = {On semidirectly closed non-aperiodic pseudovarieties of finite monoids},
url = {https://www.cambridge.org/core/services/aop-cambridge-core/content/view/BEA1B1BACC3E25204309D46CFF1E00DF/S0013091520000218a.pdf/on_semidirectly_closed_nonaperiodic_pseudovarieties_of_finite_monoids.pdf},
volume = {63},
year = {2020}
}
TY - JOUR
ID - 1733940
AU - Kaďourek, Jiří
PY - 2020
TI - On semidirectly closed non-aperiodic pseudovarieties of finite monoids
JF - Proceedings of the Edinburgh Mathematical Society
VL - 63
IS - 4
SP - 913-928
EP - 913-928
PB - Cambridge University Press
SN - 00130915
KW - pseudovarieties of finite monoids
KW - pseudovarieties of finite groups
KW - semidirect products of monoids
KW - semidirectly closed pseudovarieties
KW - finite inverse monoids
KW - finite aperiodic monoids
KW - finite R-trivial monoids
KW - finite p-groups
KW - solvable groups
UR - https://www.cambridge.org/core/services/aop-cambridge-core/content/view/BEA1B1BACC3E25204309D46CFF1E00DF/S0013091520000218a.pdf/on_semidirectly_closed_nonaperiodic_pseudovarieties_of_finite_monoids.pdf
L2 - https://www.cambridge.org/core/services/aop-cambridge-core/content/view/BEA1B1BACC3E25204309D46CFF1E00DF/S0013091520000218a.pdf/on_semidirectly_closed_nonaperiodic_pseudovarieties_of_finite_monoids.pdf
N2 - It is shown that, for every prime number p, the complete lattice of all semidirectly closed pseudovarieties of finite monoids whose intersection with the pseudovariety G of all finite groups is equal to the pseudovariety Gp of all finite p-groups has the cardinality of the continuum. Furthermore, it is shown, in addition, that the complete lattice of all semidirectly closed pseudovarieties of finite monoids whose intersection with the pseudovariety G of all finite groups is equal to the pseudovariety Gsol of all finite solvable groups has also the cardinality of the continuum.
ER -
KAĎOUREK, Jiří. On semidirectly closed non-aperiodic pseudovarieties of finite monoids. \textit{Proceedings of the Edinburgh Mathematical Society}. Cambridge University Press, 2020, roč.~63, č.~4, s.~913-928. ISSN~0013-0915. Dostupné z: https://dx.doi.org/10.1017/S0013091520000218.
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