Some Transitivity-like Concepts in Abelian Groups

Authors

Gabor Braun, Georgia Institute of TechnologyFollow
Brendan Goldsmith, Technological University DublinFollow
Ketao Gong, Hubei Engineering UniversityFollow
Lutz Strungmann, Mannheim University of Applied SciencesFollow

Document Type

Article

Rights

This item is available under a Creative Commons License for non-commercial use only

Disciplines

Applied mathematics

Publication Details

Journal of Algebra

Abstract

The classical notions of transitivity and full transitivity in Abelian p-groups have natural extensions to concepts called Krylov and weak transitivity. The interconnections between these four types of transitivity are determined for Abelian p-groups; there is a marked difference in the relationships when the prime p is equal to 2. In the final section the relationship between full and Krylov transitivity is examined in the case of mixed Abelian groups which are p-local in the sense that multiplication by an integer relatively prime to p is an automorphism.

DOI

https://doi.org/10.1016/j.jalgebra.2019.03.026

Recommended Citation

Braun, G., Goldsmith, B., Gong, K. & Strungmann, L. (2019). Some transitivity-like concepts in Abelian groups. Journal of Algebra, 529(July), pp.114-123. doi:10.1016/j.jalgebra.2019.03.026