On Finite Groups with Few Automorphism Orbits |
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Authors: | Raimundo Bastos Alex Carrazedo Dantas |
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Affiliation: | 1. Departamento de Matemática, Universidade de Brasília, Brasília, Brazilraimundo.bastosjr@yahoo.com.br;3. Departamento de Matemática, Universidade de Brasília, Brasília, Brazil |
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Abstract: | Denote by ω(G) the number of orbits of the action of Aut(G) on the finite group G. We prove that if G is a finite nonsolvable group in which ω(G) ≤5, then G is isomorphic to one of the groups A5, A6, PSL(2, 7), or PSL(2, 8). We also consider the case when ω(G) = 6 and show that, if G is a nonsolvable finite group with ω(G) = 6, then either G ≈ PSL(3, 4) or there exists a characteristic elementary abelian 2-subgroup N of G such that G/N ≈ A5. |
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Keywords: | Automorphism groups Finite groups |
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