On the class number of some real abelian number fields of prime conductors
Stanislav Jakubec (2010)
Acta Arithmetica
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Stanislav Jakubec (2010)
Acta Arithmetica
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Roblot, Xavier-François (2000)
Experimental Mathematics
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Daniel J. Madden, William Yslas Velez (1979/80)
Manuscripta mathematica
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Ágota Figula, Péter T. Nagy (2020)
Commentationes Mathematicae Universitatis Carolinae
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Our paper deals with the investigation of extensions of commutative groups by loops so that the quasigroups that result in the multiplication between cosets of the kernel subgroup are T-quasigroups. We limit our study to extensions in which the quasigroups determining the multiplication are linear functions without constant term, called linear abelian extensions. We characterize constructively such extensions with left-, right-, or inverse properties using a general construction according...
Benayed, Miloud (1998)
Journal of Lie Theory
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Luise-Charlotte Kappe, M. J. Tomkinson (1998)
Rendiconti del Seminario Matematico della Università di Padova
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Kuniaki Horie, Mitsuko Horie (2008)
Acta Arithmetica
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Jorgen Cherly (1994)
Mathematica Scandinavica
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Alexander R. Pruss (2014)
Colloquium Mathematicae
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Let G be an abelian group acting on a set X, and suppose that no element of G has any finite orbit of size greater than one. We show that every partial order on X invariant under G extends to a linear order on X also invariant under G. We then discuss extensions to linear preorders when the orbit condition is not met, and show that for any abelian group acting on a set X, there is a linear preorder ≤ on the powerset 𝓟X invariant under G and such that if A is a proper subset of B, then...
Gopal Prasad (1986)
Mathematische Annalen
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Patrik Lundström (2006)
Acta Arithmetica
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Marcin Mazur (2001)
Colloquium Mathematicae
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We prove that any Galois extension of a commutative ring with a normal basis and abelian Galois group of odd order has a self-dual normal basis. We apply this result to get a very simple proof of nonexistence of normal bases for certain extensions which are of interest in number theory.
F. OORT (1964)
Mathematische Annalen
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Carlo Toffalori (2000)
Rendiconti del Seminario Matematico della Università di Padova
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Haghighi, Mahmood (1988)
International Journal of Mathematics and Mathematical Sciences
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J. Vanderwerff (1995)
Mathematische Zeitschrift
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