Fixed-point-free automorphism groups from rings

Peter Mayr; Timothy Boykett

Fixed-point-free automorphism groups from rings

Peter Mayr, Timothy Boykett

Institute for Algebra

Research output: Contribution to journal › Article › peer-review

Abstract

Fixed-point-free automorphism groups of groups arise in Frobenius groups, planar nearrings, difference family constructions of 2--designs and the study of CP groups. Several examples of fpf automorphism groups have been derived from rings. In this note, we demonstrate that numerically, all finite examples can be so derived and that all fpf automorphism groups of abelian groups can be embedded into ring-generated examples.

Original language	English
Pages (from-to)	253-257
Number of pages	5
Journal	Southeast Asian Bulletin of Mathematics
Volume	29
Issue number	2
Publication status	Published - 2005

Fields of science

101 Mathematics
101001 Algebra
101005 Computer algebra
101013 Mathematical logic
102031 Theoretical computer science

Planar Near-rings: Theory and Application
Boykett, T. (Researcher), Ecker, J. (Researcher), Mayr, P. (Researcher), Wendt, G. (Researcher) & Pilz, G. (PI)
Austrian Science Fund
01.05.2002 → 31.05.2006
Project: Funded research › FWF - Austrian Science Fund

Cite this

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title = "Fixed-point-free automorphism groups from rings",

abstract = "Fixed-point-free automorphism groups of groups arise in Frobenius groups, planar nearrings, difference family constructions of 2--designs and the study of CP groups. Several examples of fpf automorphism groups have been derived from rings. In this note, we demonstrate that numerically, all finite examples can be so derived and that all fpf automorphism groups of abelian groups can be embedded into ring-generated examples.",

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journal = "Southeast Asian Bulletin of Mathematics",

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AU - Boykett, Timothy

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AB - Fixed-point-free automorphism groups of groups arise in Frobenius groups, planar nearrings, difference family constructions of 2--designs and the study of CP groups. Several examples of fpf automorphism groups have been derived from rings. In this note, we demonstrate that numerically, all finite examples can be so derived and that all fpf automorphism groups of abelian groups can be embedded into ring-generated examples.

M3 - Article

SN - 0129-2021

VL - 29

SP - 253

EP - 257

JO - Southeast Asian Bulletin of Mathematics

JF - Southeast Asian Bulletin of Mathematics

IS - 2

ER -

Fixed-point-free automorphism groups from rings

Abstract

Fields of science

Projects

Planar Near-rings: Theory and Application

Cite this