On groups well represented as automorphism groups of groups

Mohsen Asgharzadeh; Mohammad Golshani; Daniel Herden; Saharon Shelah

On groups well represented as automorphism groups of groups

Group Theory 2024-07-15 v1 Logic

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

Abstract

Assuming G\"{o}del'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

automorphism groups topological groups finite group theory

Cite

@article{arxiv.2407.09279,
  title  = {On groups well represented as automorphism groups of groups},
  author = {Mohsen Asgharzadeh and Mohammad Golshani and Daniel Herden and Saharon Shelah},
  journal= {arXiv preprint arXiv:2407.09279},
  year   = {2024}
}

On groups well represented as automorphism groups of groups

Abstract

Keywords

Cite

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