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Proceedings of the American Mathematical Society, 1967 Finite p-groups in which the relation (xy)P =xPyP is satisfied by all elements x, y have been called p-abelian by C. Hobby [1]. Two examples of classes of such groups are the groups of exponent p and the abelian p-groups. The purpose of this note is to show that these two classes of groups "span" the class of p-abelian groups in the following sense. If
Paul M. Weichsel
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Complexes in Abelian Groups [PDF]
Canadian Journal of Mathematics, 1954 Let G be an abelian group of order [G] ≤ ∞. Let A = {a}, B = {b}, … denote non-empty finite complexes in G. Let [A] be the number of elements of A. Finally putA + B = {a + b}.
Peter Scherk, J. H. B. Kemperman
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Abelian Groups of Fractional Operators
Computer Sciences & Mathematics Forum, 2022 Taking into count the large number of fractional operators that have been generated over the years, and considering that their number is unlikely to stop increasing at the time of writing this paper due to the recent boom of fractional calculus ...
Anthony Torres-Hernandez +2 more
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Sum structures in abelian groups
Examples and Counterexamples, 2023 Any set S of elements from an abelian group produces a graph with colored edges G(S), with its points the elements of S, and the edge between points P and Q assigned for its “color” the sum P+Q.
Robert Haas
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On Sum-Free Subsets of Abelian Groups
Axioms, 2023 In this paper, we discuss some of the key properties of sum-free subsets of abelian groups. Our discussion has been designed with a broader readership in mind and is hence not overly technical.
Renato Cordeiro de Amorim
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Entropy on abelian groups [PDF]
Advances in Mathematics, 2016 We introduce the algebraic entropy for endomorphisms of arbitrary abelian groups, appropriately modifying existing notions of entropy. The basic properties of the algebraic entropy are given, as well as various examples. The main result of this paper is the Addition Theorem showing that the algebraic entropy is additive in appropriate sense with ...
DIKRANJAN, Dikran, GIORDANO BRUNO, Anna
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On cosmall Abelian groups [PDF]
Journal of Algebra, 2007 AbstractIt is a well-known homological fact that every Abelian group G has the property that Hom(G,−) commutes with direct products. Here we investigate the ‘dual’ property: an Abelian group G is said to be cosmall if Hom(−,G) commutes with direct products.
Goldsmith, Brendan, Kolman, O.
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Perpendicularity in an Abelian Group [PDF]
International Journal of Mathematics and Mathematical Sciences, 2013 We give a set of axioms to establish a perpendicularity relation in an Abelian group and then study the existence of perpendicularities in(ℤn,+)and(ℚ+,·)and in certain other groups. Our approach provides a justification for the use of the symbol⊥denoting relative primeness in number theory and extends the domain of this convention to some degree ...
Haukkanen, Pentti +3 more
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Metric spaces related to Abelian groups
Applied General Topology, 2021 When working with a metric space, we are dealing with the additive group (R, +). Replacing (R, +) with an Abelian group (G, ∗), offers a new structure of a metric space. We call it a G-metric space and the induced topology is called the G-metric topology.
Amir Veisi, Ali Delbaznasab
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On the occurrence of elementary abelian $p$-groups as the Schur multiplier of non-abelian $p$-groups
Comptes Rendus. Mathématique, 2023 We prove that every elementary abelian $p$-group, for odd primes $p$, occurs as the Schur multiplier of some non-abelian finite $p$-group.
Rai, Pradeep K.
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