@article{911706d9380d48d3abf2c6189135d152,
title = "Normalizer quotients of symmetric groups and inner holomorphs",
abstract = "We show that every finite group T is isomorphic to a normalizer quotient NSn(H)/H for some n and a subgroup H≤Sn. We show that this holds for all large enough n≥n0(T) and also with Sn replaced by An. The two main ingredients in the proof are a recent construction due to Cornulier and Sambale of a finite group G with Out(G)≅T (for any given finite group T) and the determination of the normalizer in Sym(G) of the inner holomorph InHol(G)≤Sym(G) for any centerless indecomposable finite group G, which may be of independent interest.",
keywords = "Finite group, Inner holomorph, Normalizer quotient, Symmetric group",
author = "Alexei Entin and Tsang, {Cindy (Sin Yi)}",
note = "Publisher Copyright: {\textcopyright} 2024 Elsevier B.V.",
year = "2025",
month = jan,
doi = "10.1016/j.jpaa.2024.107839",
language = "אנגלית",
volume = "229",
journal = "Journal of Pure and Applied Algebra",
issn = "0022-4049",
publisher = "Elsevier B.V.",
number = "1",
}