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Applications of Commutator-Type Operators to $p$-Groups

Gabor Lukacs
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Abstract

For a p-group G admitting an automorphism $ϕ$ of order $p^n$ with exactly $p^m$ fixed points such that $ϕ^{p^{n-1}}$ has exactly $p^k$ fixed points, we prove that G has a fully-invariant subgroup of m-bounded nilpotency class with $(p,n,m,k)$-bounded index in G. We also establish its analogue for Lie p-rings. The proofs make use of the theory of commutator-type operators.

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Gabor Lukacs. 2001-11-02. Applications of Commutator-Type Operators to $p$-Groups. https://doi.org/10.1515/jgth.2003.007

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