Automorphisms of finite order of nilpotent groups IV
Rendiconti del Seminario Matematico della Università di Padova, Tome 136 (2016), pp. 61-68.

Let ϕ be an automorphism of finite order of the nilpotent group G of class c and m and r positive integers with ϕ m =1. Consider the two (not usually homomorphic) maps ψ and γ of G given by

ψ:gg·gϕ·gϕ 2 ·...·gϕ m-1 andγ:gg -1 ·gϕforgG.
We prove that the subgroups
X=xα:xkerψ,α Aut G,x r s0 (Gγ) s ,
Y=gγα:gG,α Aut G,(gγ) r ker γ,
X * =x r α:x ker ψ,α Aut G,x r s0 (Gψ) s ,
Y * =(gγ) r α:gG,α Aut G,(gγ) r ker γ=((Gγ) r ker γ) Aut G
of G all have finite exponent bounded in terms of c, m and r only. This yields alternative proofs of the theorem of [4] and its related bounds.

DOI : 10.4171/RSMUP/136-6
Classification : 20
Mots clés : Nilpotent group, automorphism of finite order
Wehrfritz, B.A.F. 1

1 Queen Mary University of London, LONDON, UNITED KINGDOM
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     author = {Wehrfritz, B.A.F.},
     title = {Automorphisms of finite order of nilpotent groups {IV}},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {61--68},
     publisher = {European Mathematical Society Publishing House},
     address = {Zuerich, Switzerland},
     volume = {136},
     year = {2016},
     doi = {10.4171/RSMUP/136-6},
     url = {http://www.numdam.org/articles/10.4171/RSMUP/136-6/}
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Wehrfritz, B.A.F. Automorphisms of finite order of nilpotent groups IV. Rendiconti del Seminario Matematico della Università di Padova, Tome 136 (2016), pp. 61-68. doi : 10.4171/RSMUP/136-6. http://www.numdam.org/articles/10.4171/RSMUP/136-6/

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