Kearnes, K. A. A Hamiltonian property for nilpotent algebras. (English) Zbl 0903.08001 Algebra Univers. 37, No. 4, 403-421 (1997). Applying the theory of commutators, it is shown that any finite algebra \(A\) satisfying a weak left nilpotence condition has the quasi-Hamiltonian property, i.e. all its maximal subuniverses are congruence classes. Also, conversely, if every subalgebra of \(A^2\) is quasi-Hamiltonian then \(A\) satisfies the aforementioned nilpotence condition. Reviewer: I.Chajda (Olomouc) Cited in 6 Documents MSC: 08A30 Subalgebras, congruence relations 20F18 Nilpotent groups Keywords:maximal subalgebra; quasi-Hamiltonian algebra; abelian algebra; left nilpotence; commutators; congruence classes PDFBibTeX XMLCite \textit{K. A. Kearnes}, Algebra Univers. 37, No. 4, 403--421 (1997; Zbl 0903.08001) Full Text: DOI