Let S be a finite semigroup. By Sub(S) we denote the lattice of all its subsemigroups. If A ∈ Sub(S), then by h(A) we denote the height of a subsemigroup A in the lattice Sub(S). A semigroup S is called structurally uniform if, for any A,B ∈ Sub(S) the condition h(A) = h(B) implies that A ≅ B. We present a classification of finite structurally uniform groups and commutative nilsemigroups.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 70, No. 8, pp. 1072–1084, August, 2018.
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Derech, V.D. Finite Structurally Uniform Groups and Commutative Nilsemigroups. Ukr Math J 70, 1237–1251 (2019). https://doi.org/10.1007/s11253-018-1565-1
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DOI: https://doi.org/10.1007/s11253-018-1565-1