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A. Chekhlov (2017)
On fully inert subgroups of completely decomposable groupsMathematical Notes, 101
Ulderico Dardano, Silvana Rinauro (2014)
On the ring of inertial endomorphisms of an abelian groupRicerche di Matematica, 63
Arnold (1982)
Finite Rank Torsion Free Groups and Rings in Verlag New YorkAbelian Lecture Notes Mathematics
B. Goldsmith, L. Salce, P. Zanardo (2014)
Fully inert submodules of torsion-free modules over the ring of p-adic integersColloquium Mathematicum, 136
entropy in compact topological group submitted
D. Dikranjan, A. Bruno (2011)
Functorial topologies and finite-index subgroups of abelian groupsTopology and its Applications, 158
Goldsmith (2014)
Fully inert subgroups of groupsAlgebra, 24
Ulderico Dardano, Silvana Rinauro (2012)
Inertial Automorphisms of an Abelian GroupRendiconti del Seminario Matematico della Università di Padova, 127
D. Taunt (1949)
On A-groupsMathematical Proceedings of the Cambridge Philosophical Society, 45
T. Broadbent (1970)
Abelian GroupsNature, 227
M. Bellon, C. Viallet (1998)
Algebraic EntropyCommunications in Mathematical Physics, 204
(2016)
Fully inert subgroups of completely decomposable finite rank groups and their commensurability Tomsk Mat no in
(1967)
caratterizzazione dei gruppi abelian compatti o localmente compatti nella topologia naturale Rend Sem Mat
Dikranjan (2011)
topologies and finite - index subgroups of abelian groupsTopology Appl, 14
Pierce (1963)
of primary groups in Topics in GroupsAbelian Abelian, 29
D. Dikranjan, A. Bruno, L. Salce, Simone Virili (2015)
Intrinsic algebraic entropyJournal of Pure and Applied Algebra, 219
(1954)
Infinite Michigan
Dikranjan (2016)
on groupsEntropy abelian Math, 13
V. Belyaev (1995)
Inert Subgroups in Simple Locally Finite Groups
Goldsmith (1983)
Essentially indecomposable modules over a complete discrete valuation ring Rend Sem Mat, 22
D. Arnold (1982)
Finite Rank Torsion Free Abelian Groups and Rings
Dikranjan (2009)
Algebraic entropy of endomorphisms of abelian groupsTrans Amer Math Soc, 18
Dikranjan (2013)
Fully inert subgroups of divisible groups GroupAbelian Theory, 16
(1967)
Una caratterizzazione dei gruppi abelian compatti o localmente compatti nella topologia naturale
B. Goldsmith (1983)
Essentially indecomposable modules over a complete discret valuation ringRendiconti del Seminario Matematico della Università di Padova, 70
Ulderico Dardano, D. Dikranjan, Silvana Rinauro (2017)
Inertial Properties in GroupsarXiv: Group Theory
Goldsmith (2014)
Fully inert submodules of torsion - free modules over the ring of p - adic integers Colloquium noMath, 25
D. Dikranjan, L. Salce, P. Zanardo (2014)
Fully inert subgroups of free Abelian groupsPeriodica Mathematica Hungarica, 69
I. Castellano, Ged Cook, P. Kropholler (2019)
A property of the lamplighter groupTopological Algebra and its Applications, 8
D. Dikranjan (1998)
Compactness and connectedness in topological groupsTopology and its Applications, 84
D. Dikranjan, A. Bruno, L. Salce (2010)
Adjoint algebraic entropyJournal of Algebra, 324
Ulderico Dardano, Silvana Rinauro (2013)
Inertial endomorphisms of an abelian groupAnnali di Matematica Pura ed Applicata (1923 -), 195
Dardano (2012)
Inertial automorphisms of an abelian group Rend Sem Mat
Belyaev (1994)
Inert subgroups in simple locally finite groups in Finite and locally finite groups Istanbul DordrechtAcad
D. Dikranjan, A. Bruno, L. Salce, Simone Virili (2013)
Fully inert subgroups of divisible Abelian groupsJournal of Group Theory, 16
D. Dikranjan, A. Bruno (2010)
Entropy on abelian groupsAdvances in Mathematics, 298
property of the lamplighter group to appear on Topological Algebra and its Applications this issue
Dikranjan (2014)
Fully inert subgroups of free groups noAbelian Math, 19
(2017)
Algebraic entropies for Abelian groups with applications to their endomorphism rings : a survey in Groups Modules and Model Theory - Surveys and Recent Developments pp
Mader (1981)
Basic concepts of functorial topologies in Abelian group theory in New YorkLecture Notes Mathematics, 27
B. Goldsmith, L. Salce, P. Zanardo (2014)
Fully inert subgroups of Abelian p-groups☆Journal of Algebra, 419
Carlo Casolo, Ulderico Dardano, Silvana Rinauro (2017)
Groups in which each subgroup is commensurable with a normal subgrouparXiv: Group Theory
G. Bergman, H. Lenstra (1989)
Subgroups close to normal subgroupsJournal of Algebra, 127
Monographs in
(2017)
Algebraic entropies for Abelian groups with applications to their endomorphism rings: a survey
A. Mader (1981)
Basic concepts of functorial topologies
AbstractIf H is a subgroup of an abelian group G and φ ∈ End(G), H is called φ-inert (and φ is H-inertial) if φ(H) ∩ H has finite index in the image φ(H). The notion of φ-inert subgroup arose and was investigated in a relevant way in the study of the so called intrinsic entropy of an endomorphism φ, while inertial endo-morphisms (these are endomorphisms that are H-inertial for every subgroup H) were intensively studied by Rinauro and the first named author.A subgroup H of an abelian group G is said to be fully inert if it is φ-inert for every φ ∈ End(G). This property, inspired by the “dual” notion of inertial endomorphism, has been deeply investigated for many different types of groups G. It has been proved that in some cases all fully inert subgroups of an abelian group G are commensurable with a fully invariant subgroup of G (e.g., when G is free or a direct sum of cyclic p-groups). One can strengthen the notion of fully inert subgroup by defining H to be uniformly fully inert if there exists a positive integer n such that |(H + φH)/H| ≤ n for every φ ∈ End(G). The aim of this paper is to study the uniformly fully inert subgroups of abelian groups. A natural question arising in this investigation is whether such a subgroup is commensurable with a fully invariant subgroup. This paper provides a positive answer to this question for groups belonging to several classes of abelian groups.
Topological Algebra and its Applications – de Gruyter
Published: Jan 1, 2020
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