Groups that have the same holomorph as a finite perfect group

Abstract

We describe the groups that have the same holomorph as a finite perfect group. Our results are complete for centerless groups. When the center is non-trivial, some questions remain open. The peculiarities of the general case are illustrated by a couple of examples that might be of independent interest.

19 pages - minor revisions

References in corpus (2)

• Skew braces and the Yang-Baxter equation
• The multiple holomorph of a finitely generated abelian group

Cited by in corpus (14)

• Hopf-Galois structures on extensions of degree $p^{2}q$ and skew braces of order $p^{2}q$: the cyclic Sylow $p$-subgroup case
• Bi-Skew Braces and Regular Subgroups of the Holomorph
• The Multiple Holomorphs of Finite $p$-Groups of Class Two
• On the multiple holomorph of a finite almost simple group
• On the multiple holomorph of groups of squarefree or odd prime power order
• The multiple holomorph of a semidirect product of groups having coprime exponents
• Finite $p$-groups of class two with a large multiple holomorph
• The multiple holomorph of split metacyclic $p$-groups
• Finite $p$-groups of class two with a small multiple holomorph
• Normalizer Quotients of Symmetric Groups and Inner Holomorphs
• The multiple holomorph of centerless groups
• Isomorphism of relative holomorphs and matrix similarity
• The mutually normalizing regular subgroups of the holomorph of a cyclic group of prime power order
• The NNN-Property of Cyclic Groups