Semigroups of matrices closed under conjugation by normal linear groups
Fernando C. Silva, João Araüjo · Portuguese National Funding Agency for Science, Research and Technology (RCAAP Project by FCT) · 2004
Let X be a finite set, T(X) be the monoid of all transformations on X and Sym(X) be the symmetric group on X. Recentely Levi, McAl- ister and McFadden proved that if |X| > 4, G is a normal subgroup of Sym(X) and a ∈ T(X) \ Sym(X), then ⟨g−1ag : g ∈ G⟩ = ⟨{a} ∪ G⟩ \ G. The aim of this paper is to prove a linear analogous of this result.