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Zbl 0804.20028
David, C.
$T\sb 3$-systems of finite simple groups. (English)
[J] Rend. Semin. Mat. Univ. Padova 89, 19-27 (1993). ISSN 0041-8994

Let $F\sb n$ be a free group of finite rank $n$ and let $G$ be any group. A normal subgroup $N$ of $F\sb n$ is said to be a $G$-defining subgroup if $F\sb n/N \simeq G$. The orbits for the natural action of $\text{Aut }F\sb n$ on the set of $G$-defining subgroups are said to be the $T\sb n$-systems of $G$. The author proves that the alternating group $A\sb 7$ has just one $T\sb 3$-system and that $\text{Aut }F\sb 3$ acts on the $A\sb 7$-defining subgroups as alternating or symmetric group.
[V.Mazurov (Novosibirsk)]

MSC 2000:: *20F05 Presentations of groups
20D05 Classification of simple and nonsolvable finite groups
20E05 Free nonabelian groups

Keywords: free group of rank $n$; actions; $G$-defining subgroups; $T\sb n$- systems; alternating groups; symmetric groups

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