ON GROUPS WELL REPRESENTED AS AUTOMORPHISM GROUPS OF GROUPS

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Sep 2025Embargo end date: 01 Jan 2024Publisher:Rocky Mountain Mathematics ConsortiumJournal:Journal of Commutative Algebra, volume 17 (issn: 1939-2346,

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Authors: Asgharzadeh, Mohsen; Golshani, Mohammad; Herden, Daniel; Shelah, Saharon;

doi: 10.1216/jca.2025.17.251 , 10.48550/arxiv.2407.09279

arXiv: 2407.09279

ON GROUPS WELL REPRESENTED AS AUTOMORPHISM GROUPS OF GROUPS

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Abstract

Assuming Gödel's axiom of constructibility $\bold V=\bold L,$ we present a characterization of those groups $L$ for which there exist arbitrarily large groups $H$ such that $aut(H) \cong L$. In particular, we show that it suffices to have one such group $H$ such that the size of its center is bigger than $ 2^{|L |+\aleph_0}$.

Keywords

FOS: Mathematics, Mathematics - Logic, Group Theory (math.GR), Logic (math.LO), Mathematics - Group Theory

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