Frobenius partitions in extraspecial groups
type: Item
instance of: scholarly article
title: Frobenius partitions in extraspecial groups
zbMATH Open document ID: 0919.20011
DOI: 10.1023/A:1005091820610
published in: Geometriae Dedicata
publication date: 1999-09-08T00:00:00Z
review text: Let \(G\) be a group with a partition \(\mathbf F\) into a distinguished normal subgroup \(N\) and a family \((H_i)\) of further subgroups such that \(H_iN=G\) for all \(i\in I\). The authors call \(\mathbf F\) a Frobenius partition if the \(H_i\) form an orbit under a subgroup of \(\Aut G\) (in its natural action). They use commutative division algebras to construct examples; in particular, in the finite case they obtain examples where \(N\) has order \(q^n\) and all the \(H_i\) have order \(q^{n+1}\); here \(q\) is an arbitrary odd prime power, \(n\) a natural number and \(G\) a generalized extraspecial group.
reviewed by: Dieter Jungnickel
Mathematics Subject Classification ID: 20D15
Mathematics Subject Classification ID: 05E20
Mathematics Subject Classification ID: 17A35
Mathematics Subject Classification ID: 20D30
zbMATH DE Number: 1270443
zbMATH Keywords: group partitions
zbMATH Keywords: translation transversal designs
zbMATH Keywords: Frobenius partitions
zbMATH Keywords: division algebras
zbMATH Keywords: generalized extraspecial groups
author: Norberto Gavioli
author: Virgilio Pannone
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1270443