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ON A PROBLEM OF PRAEGER AND SCHNEIDER
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 101 / Issue 1 / February 2020
- Published online by Cambridge University Press:
- 27 May 2019, pp. 80-87
- Print publication:
- February 2020
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- Article
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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 is surjective.
$$\begin{eqnarray}T=T_{\unicode[STIX]{x1D6FC}}\times T_{\unicode[STIX]{x1D6FD}}:G\longrightarrow G\times G,\quad g\mapsto (g^{-1}g^{\unicode[STIX]{x1D6FC}},g^{-1}g^{\,\unicode[STIX]{x1D6FD}})\end{eqnarray}$$
