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Enrico Jabara 《Rendiconti del Circolo Matematico di Palermo》1921,45(1):84-92
LetG be a group admitting a 4-splitting automorphism (i.e. an automorphism σ such that\(gg^\sigma g^{\sigma ^2 } g^{\sigma ^3 } = 1\) for everyg∈G). In this paper we prove that ifG≠1 is solvable with derived lengthd thenG′ is nilpotent of class not greater than (4 d?1?1)/3. 相似文献
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Enrico Jabara 《Rendiconti del Circolo Matematico di Palermo》2007,56(3):343-348
LetG be a group and ϕ an automorphism ofG. Two elementsx, y ∈ G are called ϕ-conjugate if there existsg ∈ G such thatx=g
−1
yg
θ. It is easily verified that the ϕ-conjugation is an equivalence relation; the numberR(ϕ) of ϕ-classes ofG is called the Reidemeister number of the automorphism ϕ.
In this paper we prove that if a polycyclic groupsG admits an automorphism ϕ of ordern such thatR(ϕ)<∞, thenG contains a subgroup of finite index with derived length at most 2
n−1
.
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In this note we determine the sub-sets of the set of parabolas that have measures in respect of affine group in the projective plane. 相似文献
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Enrico Jabara 《Rendiconti del Circolo Matematico di Palermo》2005,54(3):367-380
An automorphismϕ of a groupG is said to be uniform il for everyg ∈G there exists anh ∈G such thatG=h
−1
h
ρ
. It is a well-known fact that ifG is finite, an automorphism ofG is uniform if and only if it is fixed-point-free. In [7] Zappa proved that if a polycyclic groupG admits an uniform automorphism of prime orderp thenG is a finite (nilpotent)p′-group.
In this paper we continue Zappa’s work considering uniform automorphism of orderpg (p andq distinct prime numbers). In particular we prove that there exists a constantμ (depending only onp andq) such that every torsion-free polycyclic groupG admitting an uniform automorphism of orderpq is nilpotent of class at mostμ. As a consequence we prove that if a polycyclic groupG admits an uniform automorphism of orderpq thenZ
μ
(G) has finite index inG.
Al professore Guido Zappa per il suo 900 compleanno 相似文献
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