Deciding if an automorphism of an infinite soluble group is inner

Robinson, Derek J. S.

Glasgow mathematical journal, Tome 32 (1990) no. 3, pp. 265-272

Résumé

Let G be a group with a finite set of generators x1, x2,...,xn and a recursive set of defining relators in the generators. Then an endomorphism η of G is completely determined by the images of the generators , and hence by the n-tuple of words in x, (w1,...,wn). This allows the formulation of algorithmic problems about endomorphisms and automorphisms. For example, can one decide if a given n-tuple of words represents an endomorphism, and if so, an automorphism? Some results on these questions may be found in [2] and [12]. Here we shall be concerned with a similar problem: given that an n-tuple of words represents an automorphism of the group G, does there exist an algorithm which decides if the automorphism is inner?

Détail

DOI : 10.1017/S0017089500009344

Bibliographie

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