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2015β€’Journal of Taibah University for ScienceOpen access

Characterization of the automorphisms of an abelian torsion group having the weakly extension property

Mostafa Zeriouh, M’hammed Ziane, Seddik Abdelalim, Hassane Essanouni

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Abstract

In this paper, we show that if an automorphism Ξ± of an abelian torsion group, which is in fact a direct sum of its p-components, has the weak extension property then 𝛼=πœ‹β’id𝐴𝑝+𝜌, where p is a prime number, Ο€ is an invertible p-adic number and 𝜌∈Hom⁑(𝐴𝑝,𝐴1𝑝) with 𝐴1𝑝 is the first Ulm subgroup of the p-component Ap of A.

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What this paper is about

In this paper, we show that if an automorphism Ξ± of an abelian torsion group, which is in fact a direct sum of its p-components, has the weak extension property then 𝛼=πœ‹β’id𝐴𝑝+𝜌, where p is a prime number, Ο€ is an invertible p-adic number and 𝜌∈Hom⁑(𝐴𝑝,𝐴1𝑝) with 𝐴1𝑝 is the first Ulm subgroup of the p-component Ap of A.

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Available abstract

In this paper, we show that if an automorphism Ξ± of an abelian torsion group, which is in fact a direct sum of its p-components, has the weak extension property then 𝛼=πœ‹β’id𝐴𝑝+𝜌, where p is a prime number, Ο€ is an invertible p-adic number and 𝜌∈Hom⁑(𝐴𝑝,𝐴1𝑝) with 𝐴1𝑝 is the first Ulm subgroup of the p-component Ap of A.

Key concepts: Mathematics, Automorphism, Invertible matrix, Torsion (gastropod), Torsion subgroup, Abelian group, Pure mathematics, G-module

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