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- W2003288070 abstract "The Scott Conjecture, proven by Bestvina and Handel [ 2 ] says that an automorphism of a free group of rank n has fixed subgroup of rank at most n . We characterise in Theorem A below those automorphisms that realise this maximum. It follows from this characterisation, for example, that any such automorphism has linear growth. In our paper [ 3 ], we generalised the Scott Conjecture to arbitrary free products, using Kuros rank (see Section 2 below) in place of free rank; in Theorem B, we characterise those automorphisms of a free product realising the maximum. We show that in this case the growth rate is also linear. These results extend those of [ 4 ]." @default.
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- W2003288070 date "1996-05-01" @default.
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- W2003288070 title "All automorphisms of free groups with maximal rank fixed subgroups" @default.
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- W2003288070 doi "https://doi.org/10.1017/s0305004100074466" @default.
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