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T 3 -systems of finite simple groups. (English) Zbl 0804.20028
Let F n be a free group of finite rank n and let G be any group. A normal subgroup N of F n is said to be a G-defining subgroup if F n /NG. The orbits for the natural action of AutF n on the set of G-defining subgroups are said to be the T n -systems of G. The author proves that the alternating group A 7 has just one T 3 -system and that AutF 3 acts on the A 7 -defining subgroups as alternating or symmetric group.
MSC:
20F05Generators, relations, and presentations of groups
20D05Finite simple groups and their classification
20E05Free nonabelian groups