Functional graphs of abelian group endomorphisms

Abstract Extending a result by Alon, Linial, and Meshulam to abelian groups, we prove that if G is a finite abelian group of exponent m and S is a sequence of elements of G such that any subsequence of S consisting of at least $$|S| - m\ln |G|$$ elements generates G, then S is an additive basis of G . We also prove that the additive span of any l generating sets of G contains a coset of a subgroup of size at least $$|G{|^{1 - c{ \in ^l}}}$$ for certain c=c(m) and $$ \in = \in (m) < 1$$ ; we use the probabilistic method to give sharper values of c(m) and $$ \in (m)$$ in the case when G is a vector space; and we give new proofs of related known results.

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CONTINUITY OF MEASURABLE HOMOMORPHISMS

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972708000610 ◽

2008 ◽

Vol 78 (1) ◽

pp. 171-176 ◽

Cited By ~ 2

Author(s):

JANUSZ BRZDȨK

Keyword(s):

Topological Group ◽

Abelian Group ◽

Baire Property ◽

Topological Groups ◽

Locally Compact ◽

Compact Topological Group ◽

Locally Compact Topological Group

AbstractWe give some general results concerning continuity of measurable homomorphisms of topological groups. As a consequence we show that a Christensen measurable homomorphism of a Polish abelian group into a locally compact topological group is continuous. We also obtain similar results for the universally measurable homomorphisms and the homomorphisms that have the Baire property.

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Decidable characterizations of dynamical properties for additive cellular automata over a finite abelian group with applications to data encryption

Information Sciences ◽

10.1016/j.ins.2021.02.012 ◽

2021 ◽

Vol 563 ◽

pp. 183-195

Author(s):

Alberto Dennunzio ◽

Enrico Formenti ◽

Darij Grinberg ◽

Luciano Margara

Keyword(s):

Abelian Group ◽

Cellular Automata ◽

Finite Abelian Group ◽

Data Encryption ◽

Dynamical Properties

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A lattice-theoretic characterization of pure subgroups of Abelian groups

Ricerche di Matematica ◽

10.1007/s11587-021-00580-6 ◽

2021 ◽

Author(s):

M. Ferrara ◽

M. Trombetti

Keyword(s):

Abelian Group ◽

Abelian Groups ◽

Subgroup Lattice ◽

General Definition ◽

Short Paper ◽

Theoretic Characterization ◽

Definition Of

AbstractLet G be an abelian group. The aim of this short paper is to describe a way to identify pure subgroups H of G by looking only at how the subgroup lattice $$\mathcal {L}(H)$$ L ( H ) embeds in $$\mathcal {L}(G)$$ L ( G ) . It is worth noticing that all results are carried out in a local nilpotent context for a general definition of purity.

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