Abstract
It is shown that any isomorphism of the structure of the subsemigroups of two groups, one of which is structurally ordered,is a consequence only of their isomorphism or anti-isomorphism.
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K. M. Kutyev, “SL-isomorphisms of partially ordered locally-nilpotent groups,” Uspekhi Matem. Nauk,11, No. 2, 193–198 (1956).
K. M. Kutyev, “SL-isomorphisms of some classes of R-groups,” Izv. AN SSSR. Ser. Matem.,27, No. 4, 701–722 (1963).
K. M. Kutyev, “SL-isomorphisms of an ordered group,” Dokl. An SSSR,135, No. 6, 1326–1329 (1960).
L. E. Sadovskii, “Structures and isomorphisms of nilpotent groups,” Izv. AN SSSR. Ser. Matem.,29, No. 1, 172–207 (1965).
Kourovskaya Tetrad, Unsolvable Problems in Group Theory [in Russian], Second edition, Supplement, Novosibirsk (1967).
G. Birkhof, Theory of Structures [Russian translation] (1950).
W. R. Scott, “Half homomorphisms of groups,” Proc. Amer. Math. Soc.,8, No. 6, 1141–1144 (1957).
R. V. Petropavlovskaya, “Structural isomorphisms of free associative systems,” Matem. Sb.,28, No. 3, 589–602 (1951).
R. V. Petropavlovskaya, “Definability of a group by the structure of its subsystems,” Matem. Sb.,29, No. 1, 63–78 (1951).
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SL-subsemigroup lattice.
Translated from Matematicheskie Zametki, Vol. 7, No. 5, pp. 537–544, May, 1970.
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Kutyev, K.M. SL-isomorphism of a structurally ordered group. Mathematical Notes of the Academy of Sciences of the USSR 7, 326–329 (1970). https://doi.org/10.1007/BF01123841
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DOI: https://doi.org/10.1007/BF01123841