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Applications of Commutator-Type Operators to $p$-Groups | Gabor Lukacs
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2 Nov 2001 | Journal: | J. Group Theory 6 (2003), no. 1, 83--91 | Subject: | Group Theory MSC-class: 20D (Primary), 20F; 17B (Secondary) | math.GR | Abstract: | 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. | Source: | arXiv, math.GR/0111030 | Services: | Forum | Review | PDF | Favorites |
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