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Mathematical Notes, 2020
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Kolenova, E. M., Pushkova, T. A.
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Kolenova, E. M., Pushkova, T. A.
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The degree of a vertex in the kth-power graph of a finite abelian group
RECENT ADVANCES IN SCIENCES, ENGINEERING, INFORMATION TECHNOLOGY & MANAGEMENT, 2019The power graph of a given finite group is a simple undirected graph whose vertex set is the group itself, and there is an edge between any two distinct vertices if one is a power of the other. In this paper, we find a precise formula to count the degree
A. Sehgal, S. Singh
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The Balmer spectrum of the equivariant homotopy category of a finite abelian group
Inventiones Mathematicae, 2017For a finite abelian group A, we determine the Balmer spectrum of SpAω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek ...
T. Barthel +5 more
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Continuous Combinatorics of Abelian Group Actions
Memoirs of the American Mathematical Society, 2018This paper develops techniques which are used to answer a number of questions in the theory of equivalence relations generated by continuous actions of abelian groups.
Su Gao +3 more
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The Bulletin of Symbolic Logic, 2014
AbstractWe provide an introduction to methods and recent results on infinitely generated abelian groups with decidable word problem.
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AbstractWe provide an introduction to methods and recent results on infinitely generated abelian groups with decidable word problem.
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On the ring of inertial endomorphisms of an abelian group
, 2014An endomorphisms $${\varphi }$$φ of an abelian group $$A$$A is said inertial if each subgroup $$H$$H of $$A$$A has finite index in $$H+\varphi (H)$$H+φ(H). We study the ring of inertial endomorphisms of an abelian group.
Ulderico Dardano, Silvana Rinauro
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Journal of Algebra and Its Applications, 2010
An R-module RM is called morphic if M/ im α ≅ ker α for every endomorphism α of M, that is, if the dual of the Noether isomorphism theorem holds. Mostly all morphic Z-modules are determined leaving open some classes of nonsplitting mixed groups, which actually cannot be completely characterized.
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An R-module RM is called morphic if M/ im α ≅ ker α for every endomorphism α of M, that is, if the dual of the Noether isomorphism theorem holds. Mostly all morphic Z-modules are determined leaving open some classes of nonsplitting mixed groups, which actually cannot be completely characterized.
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The spanning number and the independence number of a subset of an abelian group
Let A = {a 1, a 2, …, a m } be a subset of a finite abelian group G. We call A t-independent in G, if whenever $$ \lambda _1 a_1 + \lambda _2 a_2 + ... + \lambda _m a_m = 0 $$ for some integers λ1, λ 2,…, λ m with $$ |\lambda _1 | + \lambda _2 |
B. Bajnok
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Canadian Journal of Mathematics, 1957
Throughout this note all groups areabelian, written additively. We refer to Kurosh (8; 9) for notation, terminology and theorems used without reference. We recall the notion of aserving subgroup(or pure subgroup)of a group. This is a subgroupin which for every natural numbernevery equationnx = s, s ∊can be solved provided that it can be solved in. Ifis
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Throughout this note all groups areabelian, written additively. We refer to Kurosh (8; 9) for notation, terminology and theorems used without reference. We recall the notion of aserving subgroup(or pure subgroup)of a group. This is a subgroupin which for every natural numbernevery equationnx = s, s ∊can be solved provided that it can be solved in. Ifis
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Marton’s conjecture in abelian groups with bounded torsion
Annales de la Faculté des sciences de Toulouse : MathématiquesWe prove a Freiman–Ruzsa-type theorem with polynomial bounds in arbitrary abelian groups with bounded torsion, thereby proving (in full generality) a conjecture of Marton.
W. Gowers +3 more
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