Knarr, Norbert; Stroppel, Markus J. Heisenberg groups, semifields, and translation planes. (English) Zbl 1359.12005 Beitr. Algebra Geom. 56, No. 1, 115-127 (2015). Summary: For Heisenberg groups constructed over semifields (i.e., not necessarily associative division rings), we solve the isomorphism problem and determine the automorphism groups. We show that two Heisenberg groups over semifields are isomorphic precisely if the semifields are isotopic or anti-isotopic to each other. This condition means that the corresponding translation planes are isomorphic or dual to each other. Cited in 2 Documents MSC: 12K10 Semifields 17A35 Nonassociative division algebras 20D15 Finite nilpotent groups, \(p\)-groups 20F28 Automorphism groups of groups 51A35 Non-Desarguesian affine and projective planes 51A10 Homomorphism, automorphism and dualities in linear incidence geometry Keywords:Heisenberg group; nilpotent group; automorphism; translation plane; semifield; division algebra; isotopism; autotopism PDFBibTeX XMLCite \textit{N. Knarr} and \textit{M. J. Stroppel}, Beitr. Algebra Geom. 56, No. 1, 115--127 (2015; Zbl 1359.12005) Full Text: DOI References: [1] Baer, R.: The fundamental theorems of elementary geometry. An axiomatic analysis. Trans. Amer. Math. Soc. 56, 94-129 (1944). http://www.jstor.org/stable/1990279 · Zbl 0060.32507 [2] Bruck, R.H.: Contributions to the theory of loops. Trans. Amer. Math. Soc. 60, 245-354 (1946) · Zbl 0061.02201 · doi:10.1090/S0002-9947-1946-0017288-3 [3] Cronheim, A.: \[T\] T-groups and their geometry. Illinois J. 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