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ON A PROBLEM OF PRAEGER AND SCHNEIDER

Part of: Representation theory of groups Structure and classification of infinite or finite groups

Published online by Cambridge University Press:  27 May 2019

EGLE BETTIO  and
ENRICO JABARA
EGLE BETTIO
Affiliation:
Liceo Benedetti–Tommaseo, Castello 2835, 30122 Venezia, Italy email egle.bettio@istruzione.it
ENRICO JABARA*
Affiliation:
Dipartimento di Filosofia, Università Ca’ Foscari, Dorsoduro 3484/D, 30123 Venezia, Italy email jabara@unive.it
*
✉jabara@unive.it
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Abstract

This note provides an affirmative answer to Problem 2.6 of Praeger and Schneider [‘Group factorisations, uniform automorphisms, and permutation groups of simple diagonal type’, Israel J. Math. 228(2) (2018), 1001–1023]. We will build groups $G$ (abelian, nonabelian and simple) for which there are two automorphisms $\unicode[STIX]{x1D6FC},\unicode[STIX]{x1D6FD}$ of $G$ such that the map

$$\begin{eqnarray}T=T_{\unicode[STIX]{x1D6FC}}\times T_{\unicode[STIX]{x1D6FD}}:G\longrightarrow G\times G,\quad g\mapsto (g^{-1}g^{\unicode[STIX]{x1D6FC}},g^{-1}g^{\,\unicode[STIX]{x1D6FD}})\end{eqnarray}$$
is surjective.

Keywords

uniform automorphismsfactorisations of direct productsprimitive groups

MSC classification

Primary: 20E36: Automorphisms of infinite groups
Secondary: 20D40: Products of subgroups
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 101 , Issue 1 , February 2020 , pp. 80 - 87
Copyright
© 2019 Australian Mathematical Publishing Association Inc. 

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References

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