PreprintCC BY 4.0arXiv
Extending a property of vector spaces to abelian groups
Abstract
In this note, we determine the finite abelian groups G such that for every subgroup H≤ G there exists an automorphism f∈Aut(G) with Fix(f)=H. This provides a partial answer to a problem posed by Deaconescu and Walls. Two generalizations of this problem are also proposed.
Related
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- Finite abelian subgroups of algebraic groups
BibTeX
@misc{obreja2026extending,
title = {{Extending a property of vector spaces to abelian groups}},
author = {Alexandru-Nicolae Obreja and Marius Tărnăuceanu},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07224},
eprint = {2611.07224},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07224},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Extending a property of vector spaces to abelian groups
AU - Alexandru-Nicolae Obreja
AU - Marius Tărnăuceanu
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.07224
UR - https://arxiv.org/abs/2611.07224
AB - In this note, we determine the finite abelian groups G such that for every subgroup H≤ G there exists an automorphism f∈Aut(G) with Fix(f)=H. This provides a partial answer to a problem posed by Deaconescu and Walls. Two generalizations of this problem are also proposed.
ER -