On large half-factorial sets in elementary \(p\)-groups: maximal cardinality and structural char\-ac\-ter\-i\-zation.

DOI10.1007/BF02786695zbMath1072.20032MaRDI QIDQ1775477

Alain Plagne, Wolfgang Alexander Schmid

Publication date: 3 May 2005

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

finite Abelian groupsfactorizationshalf-factorial sets

Mathematics Subject Classification ID

Arithmetic and combinatorial problems involving abstract finite groups (20D60) Commutative semigroups (20M14) Units and factorization (11R27) Finite abelian groups (20K01) Integral domains (13G05) Other analytic theory (11R47)

Related Items (9)

The set of distances in seminormal weakly Krull monoids ⋮ Half-factorial subrings of factorial domains ⋮ Weakly half-factorial sets in finite abelian groups ⋮ A NEW CHARACTERIZATION OF HALF-FACTORIAL KRULL MONOIDS ⋮ A new upper bound for the cross number of finite Abelian groups. ⋮ The set of minimal distances in Krull monoids ⋮ On half-factoriality of transfer Krull monoids ⋮ A characterization of length-factorial Krull monoids ⋮ On the maximal cardinality of half-factorial sets in cyclic groups

Cites Work

• Factorization in Dedekind domains with finite class group
• Halbgruppen mit Divisorentheorie. (Semigroups with divisor theory)
• Répartition des idéaux premiers parmi les classes d'idéaux dans un anneau de Dedekind et équidécomposition. (Distribution of prime ideals within the ideal classes in a Dedekind ring and equidecomposition.)
• On non-unique factorizations into irreducible elements
• Oscillations of error terms associated with certain arithmetical functions
• Half-factorial-domains
• Every Abelian group is a class group
• Ein quantitatives Resultat über Faktorisierungen verschiedener Länge in algebraischen Zahlkörpern. (A quantitative result on factorizations of different length in algebraic number fields)
• Systems of sets of lengths.
• Some remarks on factorization in algebraic number fields
• Finite abelian groups and factorization problems
• Remarks on factorizations in algebraic number fields
• On c-semigroups
• Half factorial domains
• Factorizations of distinct lengths in algebraic number fields
• On the distribution of algebraic numbers with prescribed factorization properties
• On the asymptotic behavior of some counting functions
• On the asymptotic behavior of some counting functions, II
• Analytic and arithmetic theory of semigroups with divisor theory
• On algebraic number fields with non-unique factorization
• A Characterization of Algebraic Number Fields with Class Number Two
• Systems of sets of lengths. II
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