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1995•Communications in AlgebraRequires access

Finite quotients of the automorphism group of a free group

Mong Lung Lang, Ka Hin Leung, Yan Loi Wong

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Abstract

The automorphism group AutFn of a free group Fn of rank n acts on the product of n copies of a group G by substituting n elements of G into the words defining an automorphism of the free group. This gives rise to an antihomomorphism from AutFnto a permutation group. We determine this antihomomorphic image of AutFn when G is the semidirect product Zp x Zq

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The automorphism group AutFn of a free group Fn of rank n acts on the product of n copies of a group G by substituting n elements of G into the words defining an automorphism of the free group. This gives rise to an antihomomorphism from AutFnto a permutation group. We determine this antihomomorphic image of AutFn when G is the semidirect product Zp x Zq

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Available abstract

The automorphism group AutFn of a free group Fn of rank n acts on the product of n copies of a group G by substituting n elements of G into the words defining an automorphism of the free group. This gives rise to an antihomomorphism from AutFnto a permutation group. We determine this antihomomorphic image of AutFn when G is the semidirect product Zp x Zq

Key concepts: Semidirect product, Mathematics, Outer automorphism group, Inner automorphism, Group (periodic table), Automorphism, p-group, Combinatorics

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