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

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

2001-11-02

arxiv.org/abs/math/0111030v1

J. Group Theory 6 (2003), no. 1, 83--91

Mathematics

Group Theory

11 pages

Scientific paper

10.1515/jgth.2003.007

For a p-group G admitting an automorphism $\phi$ of order $p^n$ with exactly
$p^m$ fixed points such that $\phi^{p^{n-1}}$ 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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